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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wpProof_Poly1305_last_block | val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g)))) | val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g)))) | let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 2017,
"start_col": 0,
"start_line": 2006
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g)))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0)
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_state",
"Prims.unit",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.Mktuple3",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRax",
"Prims.Nil",
"Prims._assert",
"Vale.X64.Decls.va_state_eq",
"Vale.X64.Decls.va_update_flags",
"Vale.X64.Decls.va_update_reg64",
"Vale.X64.Decls.va_update_ok",
"Vale.X64.Decls.va_lemma_upd_update",
"FStar.Pervasives.Native.tuple3",
"FStar.Pervasives.Native.tuple2",
"Vale.X64.State.vale_state",
"Vale.Poly1305.X64.va_lemma_Poly1305_last_block",
"Vale.Poly1305.X64.va_code_Poly1305_last_block"
] | [] | false | false | false | false | false | let va_wpProof_Poly1305_last_block va_s0 va_k =
| let va_sM, va_f0 = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM
(va_update_flags va_sM
(va_update_reg64 rRbp
va_sM
(va_update_reg64 rRbx
va_sM
(va_update_reg64 rR14
va_sM
(va_update_reg64 rR10
va_sM
(va_update_reg64 rR9
va_sM
(va_update_reg64 rR8
va_sM
(va_update_reg64 rRdx
va_sM
(va_update_reg64 rRcx
va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))
)))))));
va_lemma_norm_mods ([
va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax
])
va_sM
va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.swap_neg_mul | val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b)) | val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b)) | let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 19,
"end_line": 139,
"start_col": 0,
"start_line": 137
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> FStar.Pervasives.Lemma (ensures (- a) * b = a * (- b)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"FStar.Math.Lemmas.neg_mul_right",
"Prims.unit",
"FStar.Math.Lemmas.neg_mul_left"
] | [] | true | false | true | false | false | let swap_neg_mul a b =
| neg_mul_left a b;
neg_mul_right a b | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_codegen_success_Poly1305 | val va_codegen_success_Poly1305 : win:bool -> Tot va_pbool | val va_codegen_success_Poly1305 : win:bool -> Tot va_pbool | let va_codegen_success_Poly1305 win =
(va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi)) (va_pbool_and (if win then va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_ttrue
())))) else va_ttrue ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRcx) 184
Public) (va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Poly1305_impl ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRsi)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbp)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRdi) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue
())))))))))))))))))))))))))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 34,
"end_line": 2810,
"start_col": 0,
"start_line": 2777
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b
inp_b finish in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem
va_sM va_s0))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) : (va_quickCode int (va_code_Poly1305_impl ())) =
(va_QProc (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi;
va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem])
(va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish) (va_wpProof_Poly1305_impl key_r key_s
ctx_b inp_b finish))
//--
//-- Poly1305
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305 win =
(va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRax) (va_op_opr64_reg64 rRdi)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11)
(va_op_opr64_reg64 rRsi)) (va_CCons (if win then va_Block (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_CNil ()))))) else va_Block (va_CNil
())) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRcx) 184 Public) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rRbx)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRbp))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR11)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR12))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR14)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR15))
(va_CCons (va_code_Poly1305_impl ()) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbp) 16
Public) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_CCons
(va_code_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR12))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbp))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_DestroyHeaplets ())
(va_CNil ()))))))))))))))))))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | win: Prims.bool -> Vale.X64.Decls.va_pbool | Prims.Tot | [
"total"
] | [] | [
"Prims.bool",
"Vale.X64.Decls.va_pbool_and",
"Vale.X64.InsMem.va_codegen_success_CreateHeaplets",
"Vale.X64.InsBasic.va_codegen_success_Mov64",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Decls.va_ttrue",
"Vale.X64.Decls.va_pbool",
"Vale.X64.InsMem.va_codegen_success_Store64_buffer",
"Vale.X64.Decls.va_op_heaplet_mem_heaplet",
"Vale.X64.Decls.va_op_reg_opr64_reg64",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.InsStack.va_codegen_success_Push_Secret",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR15",
"Vale.Poly1305.X64.va_codegen_success_Poly1305_impl",
"Vale.X64.InsStack.va_codegen_success_Pop_Secret",
"Vale.X64.InsMem.va_codegen_success_DestroyHeaplets"
] | [] | false | false | false | true | false | let va_codegen_success_Poly1305 win =
| (va_pbool_and (va_codegen_success_CreateHeaplets ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR11)
(va_op_opr64_reg64 rRsi))
(va_pbool_and (if win
then
va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi)
(va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi)
(va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_op_opr64_reg64 rR8))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR9))
(va_ttrue ()))))
else va_ttrue ())
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRcx)
184
Public)
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRax
))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64
rR11))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64
rR12))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64
rR13))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64
rR14))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64
rR15))
(va_pbool_and (va_codegen_success_Poly1305_impl ()
)
(va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14)
0
Public)
(va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx)
8
Public)
(va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1
)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp)
16
Public)
(va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR15
))
(va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64
rR14))
(va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64
rR13))
(va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64
rR12))
(va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64
rRsi
))
(va_pbool_and
(va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64
rRax
))
(va_pbool_and
(va_codegen_success_Pop_Secret
(
va_op_dst_opr64_reg64
rRbp
)
)
(va_pbool_and
(
va_codegen_success_Pop_Secret
(
va_op_dst_opr64_reg64
rRbx
)
)
(
va_pbool_and
(
va_codegen_success_Mov64
(
va_op_dst_opr64_reg64
rRdi
)
(
va_op_opr64_reg64
rRax
)
)
(
va_pbool_and
(
va_codegen_success_DestroyHeaplets
()
)
(
va_ttrue
()
)
)
)
))
))))))))))))
))))))))))) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_quick_Poly1305_reduce_last | val va_quick_Poly1305_reduce_last: Prims.unit
-> (va_quickCode unit (va_code_Poly1305_reduce_last ())) | val va_quick_Poly1305_reduce_last: Prims.unit
-> (va_quickCode unit (va_code_Poly1305_reduce_last ())) | let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 63,
"end_line": 2204,
"start_col": 0,
"start_line": 2201
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | _: Prims.unit
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305_reduce_last ()) | Prims.Tot | [
"total"
] | [] | [
"Prims.unit",
"Vale.X64.QuickCode.va_QProc",
"Vale.Poly1305.X64.va_code_Poly1305_reduce_last",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Prims.Nil",
"Vale.Poly1305.X64.va_wp_Poly1305_reduce_last",
"Vale.Poly1305.X64.va_wpProof_Poly1305_reduce_last",
"Vale.X64.QuickCode.va_quickCode"
] | [] | false | false | false | false | false | let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
| (va_QProc (va_code_Poly1305_reduce_last ())
([
va_Mod_flags;
va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx;
va_Mod_reg64 rR14;
va_Mod_reg64 rRax;
va_Mod_reg64 rR10;
va_Mod_reg64 rR9;
va_Mod_reg64 rR8
])
va_wp_Poly1305_reduce_last
va_wpProof_Poly1305_reduce_last) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.mul_ineq1 | val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d)) | val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d)) | let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 5,
"end_line": 195,
"start_col": 0,
"start_line": 185
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.int -> d: Prims.nat
-> FStar.Pervasives.Lemma (requires - b < a /\ a < b /\ - d < c /\ c < d)
(ensures - b * d < a * c /\ a * c < b * d) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.op_BarBar",
"Prims.op_Equality",
"Prims.bool",
"Prims.unit",
"FStar.Math.Lemmas.lemma_abs_bound",
"FStar.Mul.op_Star",
"FStar.Math.Lemmas.lemma_mult_lt_right",
"FStar.Math.Lib.abs",
"FStar.Math.Lemmas.lemma_mult_lt_left",
"FStar.Math.Lemmas.lemma_abs_mul"
] | [] | false | false | true | false | false | let mul_ineq1 a b c d =
| if a = 0 || c = 0
then ()
else
(lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_blocks_body0 | val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))))) | val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))))) | let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 31,
"end_line": 905,
"start_col": 0,
"start_line": 822
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
va_b0: Vale.X64.Decls.va_code ->
va_s0: Vale.X64.Decls.va_state ->
va_old: Vale.X64.Decls.va_state ->
va_in_ctx_b: Vale.X64.Memory.buffer64 ->
va_in_h_in: Prims.int ->
va_in_inp_b: Vale.X64.Memory.buffer64 ->
va_in_length: Prims.int ->
va_in_n: Vale.X64.Decls.va_int_range 18446744073709551616 18446744073709551616 ->
va_in_p:
Vale.X64.Decls.va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819 ->
va_in_r: Prims.int ->
va_in_h: Prims.int ->
va_in_word_index: Prims.nat
-> Prims.Ghost (((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.int) * Prims.nat) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Vale.X64.Memory.buffer64",
"Prims.int",
"Vale.X64.Decls.va_int_range",
"Prims.nat",
"Vale.X64.QuickCodes.fuel",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.Mktuple4",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.tuple4",
"Prims.unit",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR10",
"Vale.X64.QuickCode.va_Mod_ok",
"Vale.X64.QuickCode.va_Mod_flags",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_blocks_body0",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Vale.X64.Machine_s.pow2_64",
"Vale.X64.Decls.va_mul_nat",
"Prims.op_Subtraction",
"Prims.op_Multiply",
"Prims.op_Addition",
"Vale.X64.Decls.va_get_reg64",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Prims.op_LessThan",
"Prims.op_Division",
"Prims.op_Modulus",
"Vale.X64.Machine_s.rR13",
"Vale.Def.Types_s.nat64",
"Prims.l_imp",
"Prims.l_not",
"Prims.op_LessThanOrEqual",
"Vale.X64.Memory.buffer_addr",
"Vale.X64.Memory.vuint64",
"Vale.X64.Decls.va_get_mem_heaplet",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Decls.validDstAddrs64",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Decls.va_get_mem_layout",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.Decls.validSrcAddrs64",
"Vale.Poly1305.Spec_s.modp",
"Vale.Poly1305.Util.poly1305_heap_blocks",
"Vale.X64.Decls.buffer64_as_seq",
"Vale.X64.Decls.vale_heap",
"Vale.X64.QuickCodes.precedes_wrap",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_blocks_body0",
"Vale.X64.Decls.va_expand_state"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_blocks_body0
va_b0
va_s0
va_old
va_in_ctx_b
va_in_h_in
va_in_inp_b
va_in_length
va_in_n
va_in_p
va_in_r
va_in_h
va_in_word_index
=
| let va_old = va_expand_state va_old in
let va_mods:va_mods_t =
[
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_ok; va_Mod_flags
]
in
let va_qc =
va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index
in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let h, word_index = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == (va_mul_nat va_in_n va_in_n) `op_Multiply` 4 - 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) +
va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rR12 va_sM) `op_Modulus` 4 == 0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + (va_get_reg64 rR12 va_sM) `op_Division` 4) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` (va_get_reg64 rR15 va_sM) ==
va_get_reg64 rRsi va_old + va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` (va_get_reg64 rR15 va_sM) + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b
(va_get_mem_heaplet 0 va_sM) +
8
`op_Multiply`
word_index) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rR15 va_sM) `op_Multiply` 16 <= va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM)
va_in_ctx_b
24
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_old)
va_in_inp_b
(va_in_length `op_Division` 8)
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in)
(va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n))
va_in_r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) va_in_inp_b)
word_index) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0)))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_ok; va_Mod_flags
])
va_sM
va_s0;
let h, word_index = va_g in
(va_sM, va_fM, h, word_index) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_double_mult | val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1)) | val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1)) | let pow2_double_mult n = pow2_double_sum n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 42,
"end_line": 229,
"start_col": 0,
"start_line": 229
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.nat -> FStar.Pervasives.Lemma (ensures 2 * Prims.pow2 n = Prims.pow2 (n + 1)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"FStar.Math.Lemmas.pow2_double_sum",
"Prims.unit"
] | [] | true | false | true | false | false | let pow2_double_mult n =
| pow2_double_sum n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_lt_compat | val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m) | val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m) | let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 238,
"start_col": 0,
"start_line": 235
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.nat -> m: Prims.nat
-> FStar.Pervasives.Lemma (requires m < n) (ensures Prims.pow2 m < Prims.pow2 n) (decreases m) | FStar.Pervasives.Lemma | [
"lemma",
""
] | [] | [
"Prims.nat",
"Prims.int",
"FStar.Math.Lemmas.pow2_lt_compat",
"Prims.op_Subtraction",
"Prims.unit"
] | [
"recursion"
] | false | false | true | false | false | let rec pow2_lt_compat n m =
| match m with
| 0 -> ()
| _ -> pow2_lt_compat (n - 1) (m - 1) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_le_compat | val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n)) | val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n)) | let pow2_le_compat n m =
if m < n then pow2_lt_compat n m | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 34,
"end_line": 245,
"start_col": 0,
"start_line": 244
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.nat -> m: Prims.nat
-> FStar.Pervasives.Lemma (requires m <= n) (ensures Prims.pow2 m <= Prims.pow2 n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.op_LessThan",
"FStar.Math.Lemmas.pow2_lt_compat",
"Prims.bool",
"Prims.unit"
] | [] | false | false | true | false | false | let pow2_le_compat n m =
| if m < n then pow2_lt_compat n m | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_lt_nat | val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m))) | val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m))) | let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m)) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 40,
"end_line": 286,
"start_col": 0,
"start_line": 282
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.nat -> m: Prims.nat{m <= n}
-> FStar.Pervasives.Lemma (requires a < Prims.pow2 n)
(ensures a / Prims.pow2 m < Prims.pow2 (n - m)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims._assert",
"Prims.op_Equality",
"Prims.pow2",
"FStar.Mul.op_Star",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus",
"Prims.op_Addition",
"Prims.op_Division",
"Prims.op_Modulus",
"FStar.Math.Lemmas.lemma_div_mod"
] | [] | true | false | true | false | false | let lemma_div_lt_nat a n m =
| lemma_div_mod a (pow2 m);
assert (a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n - m);
assert (pow2 n = pow2 m * pow2 (n - m)) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_minus | val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m)) | val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m)) | let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 51,
"end_line": 262,
"start_col": 0,
"start_line": 260
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.nat -> m: Prims.nat{n >= m}
-> FStar.Pervasives.Lemma (ensures Prims.pow2 n / Prims.pow2 m = Prims.pow2 (n - m)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lib.slash_star_axiom",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_minus n m =
| pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_plus | val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n) | val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n) | let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 28,
"end_line": 254,
"start_col": 0,
"start_line": 251
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m))) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.nat -> m: Prims.nat
-> FStar.Pervasives.Lemma (ensures Prims.pow2 n * Prims.pow2 m = Prims.pow2 (n + m)) (decreases n) | FStar.Pervasives.Lemma | [
"lemma",
""
] | [] | [
"Prims.nat",
"Prims.int",
"FStar.Math.Lemmas.pow2_plus",
"Prims.op_Subtraction",
"Prims.unit"
] | [
"recursion"
] | false | false | true | false | false | let rec pow2_plus n m =
| match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_lt | val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m)) | val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m)) | let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 39,
"end_line": 292,
"start_col": 0,
"start_line": 291
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.nat -> m: Prims.nat
-> FStar.Pervasives.Lemma (requires m <= n /\ a < Prims.pow2 n)
(ensures a / Prims.pow2 m < Prims.pow2 (n - m)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lemmas.lemma_div_lt_nat",
"Prims.bool",
"Prims.unit"
] | [] | false | false | true | false | false | let lemma_div_lt a n m =
| if a >= 0 then lemma_div_lt_nat a n m | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lt_multiple_is_equal | val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0) | val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0) | let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 30,
"end_line": 310,
"start_col": 0,
"start_line": 308
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.nat -> b: Prims.nat -> x: Prims.int -> n: Prims.nonzero
-> FStar.Pervasives.Lemma (requires a < n /\ b < n /\ a == b + x * n) (ensures a == b /\ x == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.int",
"Prims.nonzero",
"FStar.Math.Lemmas.bounded_multiple_is_zero",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"FStar.Mul.op_Star"
] | [] | true | false | true | false | false | let lt_multiple_is_equal a b x n =
| assert (0 * n == 0);
bounded_multiple_is_zero x n | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_qcode_Poly1305_reduce_last | val va_qcode_Poly1305_reduce_last (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_reduce_last ())) | val va_qcode_Poly1305_reduce_last (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_reduce_last ())) | let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(()))))))))))))))))))))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 30,
"end_line": 2129,
"start_col": 0,
"start_line": 2071
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ())))))))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_mods: Vale.X64.QuickCode.va_mods_t
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305_reduce_last ()) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCode.va_mods_t",
"Vale.X64.QuickCodes.qblock",
"Prims.unit",
"Prims.Cons",
"Vale.X64.Decls.va_code",
"Vale.X64.InsBasic.va_code_Mov64",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.InsBasic.va_code_Add64Wrap",
"Vale.X64.Decls.va_const_opr64",
"Vale.X64.InsBasic.va_code_Adc64Wrap",
"Vale.X64.InsBasic.va_code_Shr64",
"Vale.X64.Decls.va_const_shift_amt64",
"Vale.X64.Machine_s.rRax",
"Vale.X64.InsBasic.va_code_Sub64Wrap",
"Vale.X64.InsBasic.va_code_And64",
"Vale.X64.InsBasic.va_code_Add64",
"Prims.Nil",
"Vale.X64.Machine_s.precode",
"Vale.X64.Decls.ins",
"Vale.X64.Decls.ocmp",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.va_qPURE",
"Prims.pure_post",
"Prims.l_and",
"Prims.l_True",
"Prims.l_Forall",
"Prims.l_imp",
"Vale.Def.Words_s.nat64",
"Prims.eq2",
"Prims.int",
"Vale.Def.Types_s.ishr",
"Prims.op_Division",
"Vale.Def.Types_s.iand",
"Prims.op_Modulus",
"Prims.op_Multiply",
"Prims.b2t",
"Prims.op_LessThan",
"Vale.X64.QuickCodes.va_range1",
"Vale.Poly1305.Math.lemma_poly_bits64",
"Vale.X64.QuickCodes.va_QSeq",
"Vale.X64.InsBasic.va_quick_Mov64",
"Vale.X64.InsBasic.va_quick_Add64Wrap",
"Vale.X64.InsBasic.va_quick_Adc64Wrap",
"Vale.X64.QuickCodes.va_QBind",
"Vale.X64.QuickCodes.va_qAssertBy",
"Prims.op_Addition",
"Vale.Poly1305.Math.lowerUpper192",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.X64.Decls.va_get_reg64",
"Vale.Def.Words_s.nat128",
"Vale.Poly1305.Math.lowerUpper128_def",
"Vale.Poly1305.Math.lowerUpper128_reveal",
"Vale.Poly1305.Math.lowerUpper192_def",
"Vale.Poly1305.Math.lowerUpper192_reveal",
"Vale.X64.QuickCodes.va_QEmpty",
"Vale.Poly1305.Spec_s.mod2_128",
"Vale.Poly1305.Spec_s.modp",
"Prims.op_GreaterThanOrEqual",
"Vale.Poly1305.Math.lemma_reduce128",
"Vale.X64.InsBasic.va_quick_Shr64",
"Vale.X64.InsBasic.va_quick_Sub64Wrap",
"Vale.X64.InsBasic.va_quick_And64",
"Vale.X64.InsBasic.va_quick_Add64",
"Vale.X64.QuickCodes.quickCodes",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCode.va_quickCode",
"Vale.Poly1305.X64.va_code_Poly1305_reduce_last"
] | [] | false | false | false | false | false | let va_qcode_Poly1305_reduce_last (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
| (qblock va_mods
(fun (va_s: va_state) ->
let va_old_s:va_state = va_s in
let h:Prims.int =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s
)
(va_get_reg64 rRbx va_s))
(va_get_reg64 rRbp va_s)
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ())
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0))
(fun (va_s: va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 ==
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s))
(va_get_reg64 rR10 va_s))
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lowerUpper128_reveal ())
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lowerUpper192_reveal ())
(va_QEmpty (()))))
(let va_arg32:Vale.Def.Types_s.nat64 =
va_get_reg64 rR8 va_s
in
let va_arg31:Vale.Def.Types_s.nat64 =
va_get_reg64 rR9 va_s
in
let va_arg30:Vale.Def.Types_s.nat64 =
va_get_reg64 rR10 va_s
in
let va_arg29:Prims.int = h + 5 in
let va_arg28:Vale.Def.Types_s.nat64 =
va_get_reg64 rR14 va_old_s
in
let va_arg27:Vale.Def.Types_s.nat64 =
va_get_reg64 rRbx va_old_s
in
let va_arg26:Vale.Def.Types_s.nat64 =
va_get_reg64 rRbp va_old_s
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_reduce128 h
va_arg26
va_arg27
va_arg28
va_arg29
va_arg30
va_arg31
va_arg32)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10)
(va_const_shift_amt64 2))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR10))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax
)
(va_const_opr64 1))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14
)
(va_op_opr64_reg64 rRax))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64
rRbx)
(va_op_opr64_reg64 rRax))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64
rRax)
(va_const_opr64 0))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64
rRax)
(va_op_opr64_reg64 rR10)
)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64
rR8)
(va_op_opr64_reg64 rRax
))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64
rR9)
(va_op_opr64_reg64
rRax))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (
va_op_dst_opr64_reg64
rR14)
(va_op_opr64_reg64
rR8))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64
(va_op_dst_opr64_reg64
rRbx
)
(va_op_opr64_reg64
rR9)
)
(va_QEmpty (()
))))))))
))))))))))))))) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_mod_plus | val lemma_div_mod_plus (a k: int) (n: pos)
: Lemma ((a + k * n) / n = a / n + k /\ (a + k * n) % n = a % n) | val lemma_div_mod_plus (a k: int) (n: pos)
: Lemma ((a + k * n) / n = a / n + k /\ (a + k * n) % n = a % n) | let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 24,
"end_line": 345,
"start_col": 0,
"start_line": 342
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> k: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + k * n) / n = a / n + k /\ (a + k * n) % n = a % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_div_plus",
"Prims.l_True",
"Prims.squash",
"Prims.l_and",
"Prims.b2t",
"Prims.op_Equality",
"Prims.op_Division",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.op_Modulus",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let lemma_div_mod_plus (a k: int) (n: pos)
: Lemma ((a + k * n) / n = a / n + k /\ (a + k * n) % n = a % n) =
| lemma_div_plus a k n;
lemma_mod_plus a k n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.add_div_mod_1 | val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1) | val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1) | let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 24,
"end_line": 350,
"start_col": 0,
"start_line": 348
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + n) % n == a % n /\ (a + n) / n == a / n + 1) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_div_plus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_plus"
] | [] | true | false | true | false | false | let add_div_mod_1 a n =
| lemma_mod_plus a 1 n;
lemma_div_plus a 1 n | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_code_Poly1305_impl | val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code | val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code | let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ()))))))))))))))))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 34,
"end_line": 2348,
"start_col": 0,
"start_line": 2315
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_dummy: Prims.unit -> Vale.X64.Decls.va_code | Prims.Tot | [
"total"
] | [] | [
"Prims.unit",
"Vale.X64.Decls.va_Block",
"Vale.X64.Decls.va_CCons",
"Vale.X64.InsMem.va_code_Load64_buffer",
"Vale.X64.Decls.va_op_heaplet_mem_heaplet",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Decls.va_op_reg_opr64_reg64",
"Vale.X64.Machine_s.rRdi",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.Machine_s.rR12",
"Vale.X64.InsBasic.va_code_Mov64",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Decls.va_const_opr64",
"Vale.X64.InsBasic.va_code_And64",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.InsMem.va_code_Store64_buffer",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.InsBasic.va_code_Sub64",
"Vale.Poly1305.X64.va_code_Poly1305_blocks",
"Vale.X64.Decls.va_IfElse",
"Vale.X64.Decls.va_cmp_eq",
"Vale.X64.Decls.va_op_cmp_reg64",
"Vale.X64.Decls.va_const_cmp",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Decls.va_cmp_ne",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rR9",
"Vale.Poly1305.X64.va_code_Poly1305_last_block",
"Vale.X64.Decls.va_CNil",
"Vale.Poly1305.X64.va_code_Poly1305_reduce_last",
"Vale.Poly1305.X64.va_code_Poly1305_add_key_s",
"Vale.X64.Decls.va_code"
] | [] | false | false | false | true | false | let va_code_Poly1305_impl () =
| (va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi)
24
Public)
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi)
32
Public)
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_const_opr64 1152921487695413247))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_const_opr64 1152921487695413244))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12)
(va_op_opr64_reg64 rRcx))
(va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11)
24
Public)
(va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12)
32
Public)
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax)
(va_const_opr64 15))
(va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRdx)
(va_op_opr64_reg64 rRax))
(va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet
1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax)
56
Public)
(va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet
1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx)
64
Public)
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRcx)
(va_const_opr64 1))
(va_CCons (va_code_Poly1305_blocks ())
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet
1)
(va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi)
184
Public)
(va_CCons (va_IfElse (va_cmp_eq (
va_op_cmp_reg64 rRax
)
(va_const_cmp 1))
(va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet
1)
(va_op_dst_opr64_reg64
rR15)
(va_op_reg_opr64_reg64
rRdi)
56
Public)
(va_CCons (va_IfElse
(va_cmp_ne
(va_op_cmp_reg64
rR15
)
(va_const_cmp
0
))
(va_Block
(va_CCons
(
va_code_Load64_buffer
(
va_op_heaplet_mem_heaplet
1
)
(
va_op_dst_opr64_reg64
rRax
)
(
va_op_reg_opr64_reg64
rRdi
)
32
Public
)
(
va_CCons
(
va_code_Load64_buffer
(
va_op_heaplet_mem_heaplet
0
)
(
va_op_dst_opr64_reg64
rR8
)
(
va_op_reg_opr64_reg64
rRsi
)
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Public
)
(
va_CCons
(
va_code_Load64_buffer
(
va_op_heaplet_mem_heaplet
0
)
(
va_op_dst_opr64_reg64
rR9
)
(
va_op_reg_opr64_reg64
rRsi
)
8
Public
)
(
va_CCons
(
va_code_Poly1305_last_block
()
)
(
va_CNil
()
)
)
)
)
))
(va_Block
(va_CNil
()
))
)
(va_CCons (va_code_Poly1305_reduce_last
())
(va_CCons
(va_code_Load64_buffer
(
va_op_heaplet_mem_heaplet
1
)
(
va_op_dst_opr64_reg64
rRax
)
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va_op_reg_opr64_reg64
rRdi
)
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Public
)
(va_CCons
(
va_code_Load64_buffer
(
va_op_heaplet_mem_heaplet
1
)
(
va_op_dst_opr64_reg64
rRdx
)
(
va_op_reg_opr64_reg64
rRdi
)
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Public
)
(
va_CCons
(
va_code_Poly1305_add_key_s
()
)
(
va_CNil
()
)
)
))
))))
(va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))
)) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.cancel_mul_mod | val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0) | val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0) | let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 22,
"end_line": 367,
"start_col": 0,
"start_line": 365
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> FStar.Pervasives.Lemma (ensures a * n % n == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.unit",
"FStar.Math.Lemmas.small_mod"
] | [] | true | false | true | false | false | let cancel_mul_mod (a: int) (n: pos) =
| small_mod 0 n;
lemma_mod_plus 0 a n | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_add_key_s | val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0)))))) | val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0)))))) | let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 16,
"end_line": 2271,
"start_col": 0,
"start_line": 2256
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0)))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state
-> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.fuel",
"Prims.unit",
"FStar.Pervasives.Native.Mktuple2",
"Vale.X64.Decls.va_fuel",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.QuickCode.va_Mod_ok",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_add_key_s",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Prims.int",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.X64.Decls.va_get_reg64",
"Vale.Poly1305.Spec_s.mod2_128",
"Prims.op_Addition",
"Vale.Def.Words_s.nat128",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_add_key_s"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
| let va_mods:va_mods_t = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_add_key_s ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let () = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
(let h_in:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)
in
let key_s:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0)
in
label va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s))))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_sub_distr | val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n) | val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n) | let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 389,
"start_col": 0,
"start_line": 380
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
} | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a - b % n) % n = (a - b) % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Subtraction",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Mul.op_Star",
"Prims.op_Division",
"Prims.op_Addition",
"Prims.op_Minus",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.squash",
"FStar.Math.Lemmas.neg_mul_right",
"FStar.Math.Lemmas.lemma_div_mod"
] | [] | false | false | true | false | false | let lemma_mod_sub_distr (a b: int) (n: pos) =
| calc ( == ) {
(a - b % n) % n;
( == ) { lemma_mod_plus (a - (b % n)) (- (b / n)) n }
(a - b % n + n * (- (b / n))) % n;
( == ) { neg_mul_right n (b / n) }
(a - b % n - n * (b / n)) % n;
( == ) { lemma_div_mod b n }
(a - b) % n;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_mul_distr_r | val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n) | val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n) | let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 435,
"start_col": 0,
"start_line": 426
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
} | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures a * b % n = a * (b % n) % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_mul_distr_l"
] | [] | false | false | true | false | false | let lemma_mod_mul_distr_r (a b: int) (n: pos) =
| calc ( == ) {
(a * b) % n;
( == ) { swap_mul a b }
(b * a) % n;
( == ) { lemma_mod_mul_distr_l b a n }
((b % n) * a) % n;
( == ) { swap_mul a (b % n) }
(a * (b % n)) % n;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_sub_1 | val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b)) | val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b)) | let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 406,
"start_col": 0,
"start_line": 395
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.pos -> b: Prims.pos{a < b} -> FStar.Pervasives.Lemma (ensures (- a) % b = b - a % b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Minus",
"Prims.op_Subtraction",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.squash",
"FStar.Math.Lemmas.small_mod"
] | [] | false | false | true | false | false | let lemma_mod_sub_1 a b =
| calc ( == ) {
(- a) % b;
( == ) { lemma_mod_plus (- a) 1 b }
((- a) + 1 * b) % b;
( == ) { () }
(b - a) % b;
( == ) { small_mod (b - a) b }
b - a;
( == ) { small_mod a b }
b - a % b;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.sub_div_mod_1 | val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1) | val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1) | let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 27,
"end_line": 355,
"start_col": 0,
"start_line": 353
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a - n) % n == a % n /\ (a - n) / n == a / n - 1) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_div_plus",
"Prims.op_Minus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_plus"
] | [] | true | false | true | false | false | let sub_div_mod_1 a n =
| lemma_mod_plus a (- 1) n;
lemma_div_plus a (- 1) n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_plus | val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n) | val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n) | let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
() | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 4,
"end_line": 325,
"start_col": 0,
"start_line": 313
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> k: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + k * n) % n = a % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.unit",
"FStar.Math.Lemmas.lt_multiple_is_equal",
"Prims.op_Modulus",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.op_Subtraction",
"Prims.op_Division",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_sub_right",
"FStar.Math.Lemmas.distributivity_add_right"
] | [] | false | false | true | false | false | let lemma_mod_plus (a k: int) (n: pos) =
| calc ( == ) {
(a + k * n) % n - a % n;
( == ) { (lemma_div_mod a n;
lemma_div_mod (a + k * n) n) }
((a + k * n) - n * ((a + k * n) / n)) - (a - n * (a / n));
( == ) { () }
n * k + n * (a / n) - n * ((a + k * n) / n);
( == ) { (distributivity_add_right n k (a / n);
distributivity_sub_right n (k + a / n) ((a + k * n) / n)) }
n * (k + a / n - (a + k * n) / n);
};
lt_multiple_is_equal ((a + k * n) % n) (a % n) (k + a / n - (a + k * n) / n) n;
() | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_add_distr | val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n) | val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n) | let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 377,
"start_col": 0,
"start_line": 370
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + b % n) % n = (a + b) % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Addition",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Mul.op_Star",
"Prims.op_Division",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.squash",
"FStar.Math.Lemmas.lemma_div_mod"
] | [] | false | false | true | false | false | let lemma_mod_add_distr (a b: int) (n: pos) =
| calc ( == ) {
(a + b % n) % n;
( == ) { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b % n + n * (b / n)) % n;
( == ) { lemma_div_mod b n }
(a + b) % n;
} | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_reduce_last | val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))))) | val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))))) | let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 16,
"end_line": 2164,
"start_col": 0,
"start_line": 2147
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state
-> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.fuel",
"Prims.unit",
"FStar.Pervasives.Native.Mktuple2",
"Vale.X64.Decls.va_fuel",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.QuickCode.va_Mod_ok",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_reduce_last",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Prims.int",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.X64.Decls.va_get_reg64",
"Vale.Poly1305.Spec_s.mod2_128",
"Vale.Poly1305.Spec_s.modp",
"Vale.Poly1305.Math.lowerUpper192",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_reduce_last"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
| let va_mods:va_mods_t =
[
va_Mod_flags;
va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx;
va_Mod_reg64 rR14;
va_Mod_reg64 rRax;
va_Mod_reg64 rR10;
va_Mod_reg64 rR9;
va_Mod_reg64 rR8;
va_Mod_ok
]
in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_reduce_last ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let () = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
(let h:Prims.int =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0)
(va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0)
in
label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h))))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([
va_Mod_flags;
va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx;
va_Mod_reg64 rR14;
va_Mod_reg64 rRax;
va_Mod_reg64 rR10;
va_Mod_reg64 rR9;
va_Mod_reg64 rR8;
va_Mod_ok
])
va_sM
va_s0;
(va_sM, va_fM) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_blocks | val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))) | val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))) | let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 19,
"end_line": 1572,
"start_col": 0,
"start_line": 1503
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
va_b0: Vale.X64.Decls.va_code ->
va_s0: Vale.X64.Decls.va_state ->
r: Prims.int ->
h_in: Prims.int ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.int) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Prims.int",
"Vale.X64.Memory.buffer64",
"Vale.X64.QuickCodes.fuel",
"FStar.Pervasives.Native.Mktuple3",
"Vale.X64.Decls.va_fuel",
"Prims.unit",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_mem_heaplet",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.QuickCode.va_Mod_ok",
"Vale.X64.QuickCode.va_Mod_mem",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_blocks",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Prims.op_LessThan",
"Vale.X64.Decls.va_get_reg64",
"Vale.X64.Decls.validSrcAddrs64",
"Vale.X64.Decls.va_get_mem_heaplet",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Decls.va_get_mem_layout",
"Vale.Arch.HeapTypes_s.Public",
"Prims.op_Division",
"Vale.X64.Decls.modifies_buffer_specific",
"Vale.Def.Types_s.nat64",
"Vale.X64.Decls.buffer64_read",
"Prims.op_Addition",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Decls.va_mul_nat",
"Vale.X64.Machine_s.pow2_64",
"Vale.Poly1305.Spec_s.modp",
"Vale.Poly1305.Util.poly1305_heap_blocks",
"Vale.X64.Decls.buffer64_as_seq",
"Vale.Def.Words_s.nat64",
"Vale.X64.Decls.va_int_range",
"Prims.op_Subtraction",
"Prims.op_Multiply",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_blocks"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
| let va_mods:va_mods_t =
[
va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_ok; va_Mod_mem
]
in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_blocks ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let h = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
(let n:(va_int_range 18446744073709551616 18446744073709551616) = pow2_64 in
let p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) =
(va_mul_nat n n) `op_Multiply` 4 - 5
in
label va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM)
ctx_b
24
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0)
inp_b
((va_get_reg64 rRdx va_s0) `op_Division` 8)
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM)
0
2) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM ==
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM)) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM ==
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM)) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM ==
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM)) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM ==
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM)) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM ==
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM)) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + (va_get_reg64 rR12 va_sM) `op_Division` 4) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in
label va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in
label va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) +
va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in)
(va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n))
r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b)
((va_get_reg64 rRdx va_s0) `op_Division` 8))))))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([
va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_ok; va_Mod_mem
])
va_sM
va_s0;
let h = va_g in
(va_sM, va_fM, h) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_plus_distr_l | val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p) | val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p) | let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 32,
"end_line": 485,
"start_col": 0,
"start_line": 482
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> p: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + b) % p = (a % p + b) % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.op_Addition",
"Prims.op_Modulus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_spec2",
"Prims.op_Division",
"Prims.op_Subtraction"
] | [] | true | false | true | false | false | let lemma_mod_plus_distr_l a b p =
| let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_mul_distr_l | val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n) | val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n) | let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 423,
"start_col": 0,
"start_line": 412
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures a * b % n = (a % n) * b % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"Prims.op_Division",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.distributivity_add_left",
"FStar.Math.Lemmas.swap_mul",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.lemma_mod_plus"
] | [] | false | false | true | false | false | let lemma_mod_mul_distr_l a b n =
| calc ( == ) {
(a * b) % n;
( == ) { lemma_div_mod a n }
((n * (a / n) + a % n) * b) % n;
( == ) { distributivity_add_left (n * (a / n)) (a % n) b }
((n * (a / n)) * b + (a % n) * b) % n;
( == ) { (paren_mul_right n (a / n) b;
swap_mul ((a / n) * b) n) }
((a % n) * b + ((a / n) * b) * n) % n;
( == ) { lemma_mod_plus ((a % n) * b) ((a / n) * b) n }
((a % n) * b) % n;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.small_division_lemma_2 | val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n) | val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n) | let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 62,
"end_line": 529,
"start_col": 0,
"start_line": 529
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (requires a / n = 0) (ensures 0 <= a /\ a < n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.unit"
] | [] | true | false | true | false | false | let small_division_lemma_2 (a: int) (n: pos) =
| lemma_div_mod a n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_plus | val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k) | val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k) | let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 40,
"end_line": 340,
"start_col": 0,
"start_line": 328
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
() | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> k: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + k * n) / n = a / n + k) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_cancel_mul",
"Prims.op_Subtraction",
"Prims.op_Division",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.op_Modulus",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.distributivity_sub_right",
"Prims.squash",
"FStar.Math.Lemmas.lemma_div_mod",
"FStar.Math.Lemmas.lemma_mod_plus"
] | [] | false | false | true | false | false | let lemma_div_plus (a k: int) (n: pos) =
| calc ( == ) {
n * ((a + k * n) / n - a / n);
( == ) { distributivity_sub_right n ((a + k * n) / n) (a / n) }
n * ((a + k * n) / n) - n * (a / n);
( == ) { (lemma_div_mod (a + k * n) n;
lemma_div_mod a n) }
(a + k * n - (a + k * n) % n) - (a - a % n);
( == ) { () }
k * n - (a + k * n) % n + a % n;
( == ) { lemma_mod_plus a k n }
k * n;
};
lemma_cancel_mul ((a + k * n) / n - a / n) k n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.div_exact_r | val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n)) | val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n)) | let div_exact_r (a:int) (n:pos) = lemma_div_exact a n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 53,
"end_line": 455,
"start_col": 0,
"start_line": 455
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (requires a % n = 0) (ensures a = (a / n) * n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_div_exact",
"Prims.unit"
] | [] | true | false | true | false | false | let div_exact_r (a: int) (n: pos) =
| lemma_div_exact a n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_mod | val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p)) | val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p)) | let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 24,
"end_line": 497,
"start_col": 0,
"start_line": 495
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> p: Prims.pos
-> FStar.Pervasives.Lemma (requires a = b % p) (ensures a % p = b % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.op_Modulus",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_lt"
] | [] | true | false | true | false | false | let lemma_mod_mod a b p =
| lemma_mod_lt b p;
modulo_lemma (b % p) p | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_quick_Poly1305_add_key_s | val va_quick_Poly1305_add_key_s: Prims.unit -> (va_quickCode unit (va_code_Poly1305_add_key_s ())) | val va_quick_Poly1305_add_key_s: Prims.unit -> (va_quickCode unit (va_code_Poly1305_add_key_s ())) | let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 59,
"end_line": 2302,
"start_col": 0,
"start_line": 2300
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | _: Prims.unit
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305_add_key_s ()) | Prims.Tot | [
"total"
] | [] | [
"Prims.unit",
"Vale.X64.QuickCode.va_QProc",
"Vale.Poly1305.X64.va_code_Poly1305_add_key_s",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Prims.Nil",
"Vale.Poly1305.X64.va_wp_Poly1305_add_key_s",
"Vale.Poly1305.X64.va_wpProof_Poly1305_add_key_s",
"Vale.X64.QuickCode.va_quickCode"
] | [] | false | false | false | false | false | let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
| (va_QProc (va_code_Poly1305_add_key_s ())
([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s
va_wpProof_Poly1305_add_key_s) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_plus_distr_r | val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p) | val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p) | let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 30,
"end_line": 490,
"start_col": 0,
"start_line": 489
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> p: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + b) % p = (a + b % p) % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus_distr_l",
"Prims.unit"
] | [] | true | false | true | false | false | let lemma_mod_plus_distr_r a b p =
| lemma_mod_plus_distr_l b a p | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wpProof_Poly1305_reduce_last | val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g)))) | val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g)))) | let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 2198,
"start_col": 0,
"start_line": 2189
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g)))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0)
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_state",
"Prims.unit",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.Mktuple3",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Prims.Nil",
"Prims._assert",
"Vale.X64.Decls.va_state_eq",
"Vale.X64.Decls.va_update_flags",
"Vale.X64.Decls.va_update_reg64",
"Vale.X64.Decls.va_update_ok",
"Vale.X64.Decls.va_lemma_upd_update",
"FStar.Pervasives.Native.tuple3",
"FStar.Pervasives.Native.tuple2",
"Vale.X64.State.vale_state",
"Vale.Poly1305.X64.va_lemma_Poly1305_reduce_last",
"Vale.Poly1305.X64.va_code_Poly1305_reduce_last"
] | [] | false | false | false | false | false | let va_wpProof_Poly1305_reduce_last va_s0 va_k =
| let va_sM, va_f0 = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM
(va_update_flags va_sM
(va_update_reg64 rRbp
va_sM
(va_update_reg64 rRbx
va_sM
(va_update_reg64 rR14
va_sM
(va_update_reg64 rRax
va_sM
(va_update_reg64 rR10
va_sM
(va_update_reg64 rR9
va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([
va_Mod_flags;
va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx;
va_Mod_reg64 rR14;
va_Mod_reg64 rRax;
va_Mod_reg64 rR10;
va_Mod_reg64 rR9;
va_Mod_reg64 rR8
])
va_sM
va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_qcode_Poly1305_add_key_s | val va_qcode_Poly1305_add_key_s (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_add_key_s ())) | val va_qcode_Poly1305_add_key_s (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_add_key_s ())) | let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (())))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 52,
"end_line": 2242,
"start_col": 0,
"start_line": 2223
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ()))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_mods: Vale.X64.QuickCode.va_mods_t
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305_add_key_s ()) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCode.va_mods_t",
"Vale.X64.QuickCodes.qblock",
"Prims.unit",
"Prims.Cons",
"Vale.X64.Decls.va_code",
"Vale.X64.InsBasic.va_code_Add64Wrap",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.Machine_s.rRax",
"Vale.X64.InsBasic.va_code_Adc64Wrap",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRdx",
"Prims.Nil",
"Vale.X64.Machine_s.precode",
"Vale.X64.Decls.ins",
"Vale.X64.Decls.ocmp",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.va_QSeq",
"Vale.X64.QuickCodes.va_range1",
"Vale.X64.InsBasic.va_quick_Add64Wrap",
"Vale.X64.QuickCodes.va_QBind",
"Vale.X64.InsBasic.va_quick_Adc64Wrap",
"Vale.X64.QuickCodes.va_qPURE",
"Prims.pure_post",
"Prims.l_and",
"Prims.eq2",
"Prims.int",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.Def.Words_s.natN",
"Vale.Def.Types_s.add_wrap",
"Prims.op_GreaterThanOrEqual",
"Prims.op_Addition",
"Prims.bool",
"Prims.l_Forall",
"Prims.l_imp",
"Vale.Poly1305.Spec_s.mod2_128",
"Vale.Poly1305.Math.lemma_add_key",
"Vale.X64.QuickCodes.va_QEmpty",
"Vale.Def.Words_s.nat64",
"Vale.X64.Decls.va_get_reg64",
"Vale.X64.QuickCodes.quickCodes",
"Vale.Def.Words_s.nat128",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCode.va_quickCode",
"Vale.Poly1305.X64.va_code_Poly1305_add_key_s"
] | [] | false | false | false | false | false | let va_qcode_Poly1305_add_key_s (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
| (qblock va_mods
(fun (va_s: va_state) ->
let va_old_s:va_state = va_s in
let h_in:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)
in
let key_s:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s)
in
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx))
(fun (va_s: va_state) _ ->
let va_arg18:Vale.Def.Types_s.nat64 = va_get_reg64 rRbx va_s in
let va_arg17:Vale.Def.Types_s.nat64 = va_get_reg64 rR14 va_s in
let va_arg16:Prims.int = key_s in
let va_arg15:Vale.Def.Types_s.nat64 = va_get_reg64 rRdx va_s in
let va_arg14:Vale.Def.Types_s.nat64 = va_get_reg64 rRax va_s in
let va_arg13:Prims.int = h_in in
let va_arg12:Vale.Def.Types_s.nat64 = va_get_reg64 rRbx va_old_s in
let va_arg11:Vale.Def.Types_s.nat64 = va_get_reg64 rR14 va_old_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_add_key va_arg11
va_arg12
va_arg13
va_arg14
va_arg15
va_arg16
va_arg17
va_arg18)
(va_QEmpty (())))))) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wpProof_Poly1305_add_key_s | val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g)))) | val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g)))) | let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 2297,
"start_col": 0,
"start_line": 2290
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g)))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0)
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_state",
"Prims.unit",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.Mktuple3",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Prims.Nil",
"Prims._assert",
"Vale.X64.Decls.va_state_eq",
"Vale.X64.Decls.va_update_flags",
"Vale.X64.Decls.va_update_reg64",
"Vale.X64.Decls.va_update_ok",
"Vale.X64.Decls.va_lemma_upd_update",
"FStar.Pervasives.Native.tuple3",
"FStar.Pervasives.Native.tuple2",
"Vale.X64.State.vale_state",
"Vale.Poly1305.X64.va_lemma_Poly1305_add_key_s",
"Vale.Poly1305.X64.va_code_Poly1305_add_key_s"
] | [] | false | false | false | false | false | let va_wpProof_Poly1305_add_key_s va_s0 va_k =
| let va_sM, va_f0 = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM
(va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_definition_lemma_1 | val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1) | val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1) | let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 5,
"end_line": 548,
"start_col": 0,
"start_line": 544
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> m: Prims.int{a - b < m * b}
-> FStar.Pervasives.Lemma (ensures m > a / b - 1) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"FStar.Mul.op_Star",
"Prims.op_Division",
"Prims.bool",
"FStar.Math.Lemmas.multiplication_order_lemma",
"Prims.unit",
"FStar.Math.Lemmas.division_propriety"
] | [] | false | false | true | false | false | let division_definition_lemma_1 a b m =
| if a / b - 1 < 0
then ()
else
(division_propriety a b;
multiplication_order_lemma m (a / b - 1) b) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_last_block | val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))))))))) | val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))))))))) | let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 16,
"end_line": 1962,
"start_col": 0,
"start_line": 1931
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state
-> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.fuel",
"Prims.unit",
"FStar.Pervasives.Native.Mktuple2",
"Vale.X64.Decls.va_fuel",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRax",
"Vale.X64.QuickCode.va_Mod_ok",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_last_block",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Prims.op_LessThan",
"Vale.X64.Decls.va_get_reg64",
"Prims.int",
"Vale.Poly1305.Spec_s.modp",
"Prims.op_Multiply",
"Prims.op_Addition",
"Prims.op_Modulus",
"Vale.Poly1305.Math.lowerUpper192",
"Vale.Poly1305.Math.lowerUpper128",
"Prims.pos",
"Prims.pow2",
"Vale.X64.Machine_s.rR15",
"Vale.Def.Words_s.nat128",
"Vale.X64.Machine_s.rR11",
"Vale.Def.Words_s.nat64",
"Vale.X64.Decls.va_int_range",
"Prims.op_Subtraction",
"Vale.X64.Decls.va_mul_nat",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_last_block"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_last_block va_b0 va_s0 =
| let va_mods:va_mods_t =
[
va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax;
va_Mod_ok
]
in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_last_block ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let () = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
(let n:(va_int_range 18446744073709551616 18446744073709551616) = 18446744073709551616 in
let p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) =
(va_mul_nat n n) `op_Multiply` 4 - 5
in
let r1:nat64 = va_get_reg64 rRax va_s0 in
let r:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1
in
let hBlocks:Prims.int =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0)
(va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0)
in
let inpLast:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0)
in
label va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 ((va_get_reg64 rR15 va_sM) `op_Multiply` 8) in
label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14
va_sM)
(va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)
in
label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast ==
Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp hBlocks + padLast +
inpLast
`op_Modulus`
padLast)
`op_Multiply`
r))))))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([
va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax;
va_Mod_ok
])
va_sM
va_s0;
(va_sM, va_fM) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mul_sub_distr | val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c)) | val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c)) | let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 32,
"end_line": 445,
"start_col": 0,
"start_line": 444
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> c: Prims.int
-> FStar.Pervasives.Lemma (ensures a * b - a * c = a * (b - c)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"FStar.Math.Lemmas.distributivity_sub_right",
"Prims.unit"
] | [] | true | false | true | false | false | let lemma_mul_sub_distr a b c =
| distributivity_sub_right a b c | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.reveal_logand128 | val reveal_logand128 (x y: nat128)
: Lemma (requires True) (ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y) | val reveal_logand128 (x y: nat128)
: Lemma (requires True) (ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y) | let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 46,
"end_line": 2308,
"start_col": 0,
"start_line": 2305
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//-- | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: Vale.X64.Machine_s.nat128 -> y: Vale.X64.Machine_s.nat128
-> FStar.Pervasives.Lemma (ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand x y) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Vale.X64.Machine_s.nat128",
"Vale.Def.TypesNative_s.reveal_iand",
"Prims.unit",
"Prims.l_True",
"Prims.squash",
"Prims.eq2",
"Prims.int",
"Prims.l_or",
"Prims.l_and",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"Prims.op_LessThan",
"Vale.Def.Words_s.pow2_128",
"FStar.UInt.size",
"Vale.Def.Types_s.iand",
"FStar.UInt.logand",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let reveal_logand128 (x y: nat128)
: Lemma (requires True) (ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y) =
| Vale.Def.TypesNative_s.reveal_iand 128 x y | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_definition_lemma_2 | val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1) | val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1) | let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 44,
"end_line": 553,
"start_col": 0,
"start_line": 551
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> m: Prims.int{m * b <= a}
-> FStar.Pervasives.Lemma (ensures m < a / b + 1) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Mul.op_Star",
"FStar.Math.Lemmas.multiplication_order_lemma",
"Prims.op_Addition",
"Prims.op_Division",
"Prims.unit",
"FStar.Math.Lemmas.division_propriety"
] | [] | true | false | true | false | false | let division_definition_lemma_2 a b m =
| division_propriety a b;
multiplication_order_lemma (a / b + 1) m b | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_spec | val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p) | val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p) | let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 467,
"start_col": 0,
"start_line": 460
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> p: Prims.pos -> FStar.Pervasives.Lemma (ensures a / p = (a - a % p) / p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Division",
"Prims.op_Subtraction",
"Prims.op_Modulus",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Mul.op_Star",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.cancel_mul_div"
] | [] | false | false | true | false | false | let lemma_mod_spec a p =
| calc ( == ) {
(a - a % p) / p;
( == ) { lemma_div_mod a p }
(p * (a / p)) / p;
( == ) { cancel_mul_div (a / p) p }
a / p;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_spec2 | val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p) | val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p) | let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 478,
"start_col": 0,
"start_line": 471
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> p: Prims.pos
-> FStar.Pervasives.Lemma
(ensures
(let q = (a - a % p) / p in
a = a % p + q * p)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Addition",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.op_Division",
"Prims.op_Subtraction",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_spec",
"Prims.squash",
"FStar.Math.Lemmas.lemma_div_mod"
] | [] | false | false | true | false | false | let lemma_mod_spec2 a p =
| calc ( == ) {
(a % p) + ((a - (a % p)) / p) * p;
( == ) { lemma_mod_spec a p }
(a % p) + (a / p) * p;
( == ) { lemma_div_mod a p }
a;
} | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_quick_Poly1305_impl | val va_quick_Poly1305_impl (key_r key_s: nat128) (ctx_b inp_b: buffer64) (finish: nat64)
: (va_quickCode int (va_code_Poly1305_impl ())) | val va_quick_Poly1305_impl (key_r key_s: nat128) (ctx_b inp_b: buffer64) (finish: nat64)
: (va_quickCode int (va_code_Poly1305_impl ())) | let va_quick_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) : (va_quickCode int (va_code_Poly1305_impl ())) =
(va_QProc (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi;
va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem])
(va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish) (va_wpProof_Poly1305_impl key_r key_s
ctx_b inp_b finish)) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 24,
"end_line": 2742,
"start_col": 0,
"start_line": 2735
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b
inp_b finish in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem
va_sM va_s0))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
key_r: Vale.X64.Machine_s.nat128 ->
key_s: Vale.X64.Machine_s.nat128 ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64 ->
finish: Vale.X64.Memory.nat64
-> Vale.X64.QuickCode.va_quickCode Prims.int (Vale.Poly1305.X64.va_code_Poly1305_impl ()) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Machine_s.nat128",
"Vale.X64.Memory.buffer64",
"Vale.X64.Memory.nat64",
"Vale.X64.QuickCode.va_QProc",
"Prims.int",
"Vale.Poly1305.X64.va_code_Poly1305_impl",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_mem_heaplet",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRax",
"Vale.X64.QuickCode.va_Mod_mem",
"Prims.Nil",
"Vale.Poly1305.X64.va_wp_Poly1305_impl",
"Vale.Poly1305.X64.va_wpProof_Poly1305_impl",
"Vale.X64.QuickCode.va_quickCode"
] | [] | false | false | false | false | false | let va_quick_Poly1305_impl (key_r key_s: nat128) (ctx_b inp_b: buffer64) (finish: nat64)
: (va_quickCode int (va_code_Poly1305_impl ())) =
| (va_QProc (va_code_Poly1305_impl ())
([
va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem
])
(va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish)
(va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish)) | false |
Steel.ST.HigherArray.fsti | Steel.ST.HigherArray.ptrdiff | val ptrdiff (#t: _) (#p0 #p1: perm) (#s0 #s1: Ghost.erased (Seq.seq t)) (a0 a1: array t)
: ST UP.t
((pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(fun _ -> (pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(base (ptr_of a0) == base (ptr_of a1) /\ UP.fits (offset (ptr_of a0) - offset (ptr_of a1)))
(fun r -> UP.v r == offset (ptr_of a0) - offset (ptr_of a1)) | val ptrdiff (#t: _) (#p0 #p1: perm) (#s0 #s1: Ghost.erased (Seq.seq t)) (a0 a1: array t)
: ST UP.t
((pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(fun _ -> (pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(base (ptr_of a0) == base (ptr_of a1) /\ UP.fits (offset (ptr_of a0) - offset (ptr_of a1)))
(fun r -> UP.v r == offset (ptr_of a0) - offset (ptr_of a1)) | let ptrdiff (#t:_) (#p0 #p1:perm) (#s0 #s1:Ghost.erased (Seq.seq t))
(a0:array t)
(a1:array t)
: ST UP.t
(pts_to a0 p0 s0 `star` pts_to a1 p1 s1)
(fun _ -> pts_to a0 p0 s0 `star` pts_to a1 p1 s1)
(base (ptr_of a0) == base (ptr_of a1) /\ UP.fits (offset (ptr_of a0) - offset (ptr_of a1)))
(fun r -> UP.v r == offset (ptr_of a0) - offset (ptr_of a1))
= let (| pt0, len0 |) = a0 in
let (| pt1, len1 |) = a1 in
rewrite
(pts_to a0 _ _)
(pts_to (| pt0, len0 |) p0 s0);
rewrite
(pts_to a1 _ _)
(pts_to (| pt1, len1 |) p1 s1);
let res = ptrdiff_ptr pt0 len0 pt1 len1 in
rewrite
(pts_to (| pt0, len0 |) p0 s0)
(pts_to a0 _ _);
rewrite
(pts_to (| pt1, len1 |) p1 s1)
(pts_to a1 _ _);
return res | {
"file_name": "lib/steel/Steel.ST.HigherArray.fsti",
"git_rev": "f984200f79bdc452374ae994a5ca837496476c41",
"git_url": "https://github.com/FStarLang/steel.git",
"project_name": "steel"
} | {
"end_col": 14,
"end_line": 636,
"start_col": 0,
"start_line": 613
} | (*
Copyright 2022 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module Steel.ST.HigherArray
/// C arrays of universe 1 elements.
///
/// - Due to a limitation on the universe for selectors, no selector
/// version can be defined for universe 1.
/// - Due to F* universes not being cumulative, arrays of universe 0
/// elements need to be defined in a separate module.
module P = Steel.FractionalPermission
module US = FStar.SizeT
module UP = FStar.PtrdiffT
open Steel.ST.Util
/// NOTE: This module is slated to have primitive Karamel extraction
/// (except for definitions meant to be inlined.)
/// An abstract type to represent a base array (whole allocation
/// unit), exposed for proof purposes only
[@@erasable]
val base_t (elt: Type u#a) : Tot Type0
val base_len (#elt: Type) (b: base_t elt) : GTot nat
/// An abstract type to represent a C pointer, as a base and an offset
/// into its base
[@@noextract_to "krml"] // primitive
val ptr ([@@@unused] elt: Type u#a) : Type0
[@@noextract_to "krml"]
val null_ptr (elt: Type u#a) : ptr elt
// TODO: turn into a stateful operation to avoid comparing dangling pointers
[@@noextract_to "krml"]
val is_null_ptr (#elt: Type u#a) (p: ptr elt) : Pure bool
(requires True)
(ensures (fun res -> res == true <==> p == null_ptr elt))
val base (#elt: Type) (p: ptr elt) : Tot (base_t elt)
val offset (#elt: Type) (p: ptr elt) : Ghost nat (requires True) (ensures (fun offset -> offset <= base_len (base p)))
val ptr_base_offset_inj (#elt: Type) (p1 p2: ptr elt) : Lemma
(requires (
base p1 == base p2 /\
offset p1 == offset p2
))
(ensures (
p1 == p2
))
val base_len_null_ptr (elt: Type u#a) : Lemma
(base_len (base (null_ptr elt)) == 0)
[SMTPat (base_len (base (null_ptr elt)))]
/// A concrete type to represent a C array, as a C pointer and a ghost
/// array length. By virtue of the length being ghost, Karamel will
/// extract this type as just ptr, but to inline the definition of
/// this type, we use standard dependent pairs instead of a custom
/// record type.
inline_for_extraction
[@@noextract_to "krml"]
let array ([@@@strictly_positive] elt: Type u#a) : Tot Type0 =
(p: ptr elt & (length: Ghost.erased nat {offset p + length <= base_len (base p)}))
inline_for_extraction
[@@noextract_to "krml"]
let null (#a: Type u#a) : array a
= (| null_ptr a, Ghost.hide 0 |)
/// This will extract to "let p = a"
inline_for_extraction
[@@noextract_to "krml"]
let ptr_of
(#elt: Type)
(a: array elt)
: Tot (ptr elt)
= match a with // dfst is not marked inline_for_extraction, so we need to reimplement it
| (| p, _ |) -> p
inline_for_extraction
[@@noextract_to "krml"]
let is_null (#a: Type u#a) (p: array a) : Pure bool
(requires True)
(ensures (fun res -> res == true <==> p == null))
= is_null_ptr (ptr_of p)
let length (#elt: Type) (a: array elt) : GTot nat =
dsnd a
val length_fits (#elt: Type) (a: array elt) : Lemma (US.fits (length a))
/// A Steel separation logic heap predicate to describe that an array
/// a points to some element sequence s with some permission p. vprop
/// limits the universe to at most 1 (because of the universe of the
/// heap.)
val pts_to
(#elt: Type u#1) (a: array elt)
(p: P.perm)
([@@@ smt_fallback ] s: Seq.seq elt)
: Tot vprop
/// A stateful lemma to relate the size of an array with the size
/// of the element sequence it points to
val pts_to_length
(#opened: _)
(#elt: Type u#1)
(#p: P.perm)
(a: array elt)
(s: Seq.seq elt)
: STGhost unit opened
(pts_to a p s)
(fun _ -> pts_to a p s)
(True)
(fun _ -> Seq.length s == length a)
val pts_to_not_null
(#opened: _)
(#elt: Type u#1)
(#p: P.perm)
(a: array elt)
(s: Seq.seq elt)
: STGhost unit opened
(pts_to a p s)
(fun _ -> pts_to a p s)
(True)
(fun _ -> a =!= null)
/// An injectivity property, needed only to define a selector. Such a
/// selector can be only defined in universe 0, and universes are not
/// cumulative, so we need to define a separate module for arrays of
/// universe 0 elements with selectors, reusing definitions from this
/// interface, but we do not want to use `friend`.
val pts_to_inj
(#elt: Type u#1) (a: array elt)
(p1: P.perm)
(s1: Seq.seq elt)
(p2: P.perm)
(s2: Seq.seq elt)
(m: mem)
: Lemma
(requires (
interp (hp_of (pts_to a p1 s1)) m /\
interp (hp_of (pts_to a p2 s2)) m
))
(ensures (
s1 == s2
))
/// Allocating a new array of size n, where each cell is initialized
/// with value x. We expose a pointer version for extraction purposes
[@@noextract_to "krml"] // primitive
val malloc_ptr
(#elt: Type)
(x: elt)
(n: US.t)
: STT(a: ptr elt { base_len (base a) == US.v n /\ offset a == 0 })
emp
(fun a -> pts_to (| a, Ghost.hide (US.v n) |) P.full_perm (Seq.create (US.v n) x))
/// Allocating a new array of size n, where each cell is initialized
/// with value x
let is_full_array (#elt: Type) (a: array elt) : Tot prop =
length a == base_len (base (ptr_of a))
inline_for_extraction
[@@noextract_to "krml"]
let malloc
(#elt: Type)
(x: elt)
(n: US.t)
: ST (array elt)
emp
(fun a -> pts_to a P.full_perm (Seq.create (US.v n) x))
(True)
(fun a ->
length a == US.v n /\
is_full_array a
)
= let p = malloc_ptr x n in
let a : array elt = (| p, Ghost.hide (US.v n) |) in
rewrite
(pts_to _ _ _)
(pts_to a _ _);
return a
/// Freeing a full array. Same here, we expose a ptr version for extraction purposes only
[@@ noextract_to "krml"; // primitive
warn_on_use "Steel.HigherArray.free is currently unsound in the presence of zero-size subarrays, have you collected them all?"]
val free_ptr
(#elt: Type)
(#s: Ghost.erased (Seq.seq elt))
(a: ptr elt { offset a == 0 })
: STT unit
(pts_to (| a, Ghost.hide #nat (base_len (base a)) |) P.full_perm s)
(fun _ -> emp)
inline_for_extraction
[@@ noextract_to "krml";
warn_on_use "Steel.HigherArray.free is currently unsound in the presence of zero-size subarrays, have you collected them all?"]
let free
(#elt: Type)
(a: array elt)
: ST unit
(exists_ (pts_to a P.full_perm))
(fun _ -> emp)
(
is_full_array a
)
(fun _ -> True)
= let (| p, v |) = a in
let _ : squash (offset p == 0) = () in
let s = elim_exists () in
rewrite (pts_to _ _ _)
(pts_to (| p, Ghost.hide (base_len (base p)) |) full_perm s);
free_ptr p
/// Sharing and gathering permissions on an array. Those only
/// manipulate permissions, so they are nothing more than stateful
/// lemmas.
val share
(#opened: _)
(#elt: Type)
(#x: Seq.seq elt)
(a: array elt)
(p p1 p2: P.perm)
: STGhost unit opened
(pts_to a p x)
(fun _ -> pts_to a p1 x `star` pts_to a p2 x)
(p == p1 `P.sum_perm` p2)
(fun _ -> True)
val gather
(#opened: _)
(#elt: Type)
(a: array elt)
(#x1: Seq.seq elt) (p1: P.perm)
(#x2: Seq.seq elt) (p2: P.perm)
: STGhost unit opened
(pts_to a p1 x1 `star` pts_to a p2 x2)
(fun _ -> pts_to a (p1 `P.sum_perm` p2) x1)
(True)
(fun _ -> x1 == x2)
/// Reading the i-th element of an array a.
/// TODO: we should also provide an atomic version for small types.
[@@noextract_to "krml"] // primitive
val index_ptr
(#t: Type) (#p: P.perm)
(a: ptr t)
(#len: Ghost.erased nat { offset a + len <= base_len (base a) })
(#s: Ghost.erased (Seq.seq t))
(i: US.t)
: ST t
(pts_to (| a, len |) p s)
(fun _ -> pts_to (| a, len |) p s)
(US.v i < Ghost.reveal len \/ US.v i < Seq.length s)
(fun res -> Seq.length s == Ghost.reveal len /\ US.v i < Seq.length s /\ res == Seq.index s (US.v i))
inline_for_extraction
[@@noextract_to "krml"] // primitive
let index
(#t: Type) (#p: P.perm)
(a: array t)
(#s: Ghost.erased (Seq.seq t))
(i: US.t)
: ST t
(pts_to a p s)
(fun _ -> pts_to a p s)
(US.v i < length a \/ US.v i < Seq.length s)
(fun res -> Seq.length s == length a /\ US.v i < Seq.length s /\ res == Seq.index s (US.v i))
= rewrite
(pts_to _ _ _)
(pts_to (| (ptr_of a), (dsnd a) |) p s);
let res = index_ptr (ptr_of a) i in
rewrite
(pts_to _ _ _)
(pts_to a p s);
return res
/// Writing the value v at the i-th element of an array a.
/// TODO: we should also provide an atomic version for small types.
[@@noextract_to "krml"] // primitive
val upd_ptr
(#t: Type)
(a: ptr t)
(#len: Ghost.erased nat { offset a + len <= base_len (base a) })
(#s: Ghost.erased (Seq.seq t))
(i: US.t { US.v i < Seq.length s })
(v: t)
: STT unit
(pts_to (| a, len |) P.full_perm s)
(fun res -> pts_to (| a, len |) P.full_perm (Seq.upd s (US.v i) v))
inline_for_extraction
[@@noextract_to "krml"]
let upd
(#t: Type)
(a: array t)
(#s: Ghost.erased (Seq.seq t))
(i: US.t { US.v i < Seq.length s })
(v: t)
: STT unit
(pts_to a P.full_perm s)
(fun res -> pts_to a P.full_perm (Seq.upd s (US.v i) v))
= rewrite
(pts_to _ _ _)
(pts_to (| ptr_of a, (dsnd a) |) _ s);
upd_ptr (ptr_of a) i v;
rewrite
(pts_to _ _ _)
(pts_to _ _ _)
/// An array a1 is adjacent to an array a2 if and only if they have
/// the same base array and the end of a1 coincides with the beginning
/// of a2
let adjacent (#elt: Type) (a1 a2: array elt) : Tot prop =
base (ptr_of a1) == base (ptr_of a2) /\
offset (ptr_of a1) + (length a1) == offset (ptr_of a2)
/// If two arrays are adjacent, then we can compute their merge, with
/// their combined lengths. By virtue of the length being ghost,
/// Karamel will extract it as "let y = a1"
inline_for_extraction
[@@noextract_to "krml"]
let merge (#elt: Type) (a1: array elt) (a2: Ghost.erased (array elt))
: Pure (array elt)
(requires (adjacent a1 a2))
(ensures (fun y -> length y == length a1 + length a2))
= (| ptr_of a1, Ghost.hide (length a1 + length a2) |)
/// Adjacency and merging are associative.
let merge_assoc (#elt: Type) (a1 a2 a3: array elt) : Lemma
(requires (
(adjacent a1 a2 /\ adjacent a2 a3) \/
(adjacent a1 a2 /\ adjacent (merge a1 a2) a3) \/
(adjacent a2 a3 /\ adjacent a1 (merge a2 a3))
))
(ensures (
adjacent (merge a1 a2) a3 /\ adjacent a1 (merge a2 a3) /\
merge (merge a1 a2) a3 == merge a1 (merge a2 a3)
))
= ()
/// A shortcut to combine adjacency and merging
let merge_into (#elt: Type) (a1 a2 a: array elt) : Tot prop =
adjacent a1 a2 /\
merge a1 a2 == a
/// Spatial merging of two arrays, expressed in terms of `merge`.
val ghost_join
(#opened: _)
(#elt: Type)
(#x1 #x2: Seq.seq elt)
(#p: P.perm)
(a1 a2: array elt)
(h: squash (adjacent a1 a2))
: STGhostT unit opened
(pts_to a1 p x1 `star` pts_to a2 p x2)
(fun res -> pts_to (merge a1 a2) p (x1 `Seq.append` x2))
/// Spatial merging, combining the use of `merge` and the call to the
/// stateful lemma. Since the only operations are calls to stateful
/// lemmas and pure computations, the overall computation is atomic
/// and unobservable, so can be used anywhere in atomic contexts. By
/// virtue of the length being ghost, Karamel will extract this to
/// "let res = a1"
inline_for_extraction // this will extract to "let res = a1"
[@@noextract_to "krml"]
let join
(#opened: _)
(#elt: Type)
(#x1 #x2: Ghost.erased (Seq.seq elt))
(#p: P.perm)
(a1: array elt)
(a2: Ghost.erased (array elt))
: STAtomicBase (array elt) false opened Unobservable
(pts_to a1 p x1 `star` pts_to a2 p x2)
(fun res -> pts_to res p (x1 `Seq.append` x2))
(adjacent a1 a2)
(fun res -> merge_into a1 a2 res)
= let _ : squash (adjacent a1 a2) = () in
ghost_join a1 a2 ();
let res = merge a1 a2 in
rewrite
(pts_to (merge a1 (Ghost.hide (Ghost.reveal a2))) p (x1 `Seq.append` x2))
(pts_to res p (x1 `Seq.append` x2));
return res
/// Computing the left-hand-side part of splitting an array a at
/// offset i. By virtue of the length being ghost, Karamel will
/// extract this to "let y = a"
inline_for_extraction // this will extract to "let y = a"
[@@noextract_to "krml"]
let split_l (#elt: Type) (a: array elt)
(i: Ghost.erased US.t)
: Pure (array elt)
(requires (US.v i <= length a))
(ensures (fun y -> True))
= (| ptr_of a, Ghost.hide (US.v i) |)
/// C pointer arithmetic to compute (p+off), shifting a pointer p by
/// offset off. TODO: replace this with a Ghost definition and a
/// STAtomicBase Unobservable operation with the corresponding
/// permission.
[@@noextract_to "krml"] // primitive
val ptr_shift
(#elt: Type)
(p: ptr elt)
(off: US.t)
: Pure (ptr elt)
(requires (offset p + US.v off <= base_len (base p)))
(ensures (fun p' ->
base p' == base p /\
offset p' == offset p + US.v off
))
let ptr_shift_zero
(#elt: Type)
(p: ptr elt)
: Lemma
(ptr_shift p 0sz == p)
= ptr_base_offset_inj (ptr_shift p 0sz) p
/// Computing the right-hand-side part of splitting an array a at
/// offset i.
inline_for_extraction
[@@noextract_to "krml"]
let split_r (#elt: Type) (a: array elt)
(i: US.t)
: Pure (array elt)
(requires (US.v i <= length a))
(ensures (fun y -> merge_into (split_l a i) y a))
= (| ptr_shift (ptr_of a) i, Ghost.hide (length a - US.v i) |)
/// Splitting an array a at offset i, as a stateful lemma expressed in
/// terms of split_l, split_r. This stateful lemma returns a proof
/// that offset i is in bounds of the value sequence, which is needed to
/// typecheck the post-resource.
val ghost_split
(#opened: _)
(#elt: Type)
(#x: Seq.seq elt)
(#p: P.perm)
(a: array elt)
(i: US.t)
: STGhost (squash (US.v i <= length a /\ US.v i <= Seq.length x)) opened
(pts_to a p x)
(fun res ->
pts_to (split_l a i) p (Seq.slice x 0 (US.v i)) `star`
pts_to (split_r a i) p (Seq.slice x (US.v i) (Seq.length x)))
(US.v i <= length a)
(fun res ->
x == Seq.append (Seq.slice x 0 (US.v i)) (Seq.slice x (US.v i) (Seq.length x))
)
/// NOTE: we could implement a STAtomicBase Unobservable "split"
/// operation, just like "join", but we don't want it to return a pair
/// of arrays. For now we settle on explicit use of split_l, split_r.
/// Copies the contents of a0 to a1
let blit_post
(#t:_) (s0 s1:Ghost.erased (Seq.seq t))
(src:array t)
(idx_src: US.t)
(dst:array t)
(idx_dst: US.t)
(len: US.t)
(s1' : Seq.seq t)
: Tot prop
=
US.v idx_src + US.v len <= length src /\
US.v idx_dst + US.v len <= length dst /\
length src == Seq.length s0 /\
length dst == Seq.length s1 /\
Seq.length s1' == Seq.length s1 /\
Seq.slice s1' (US.v idx_dst) (US.v idx_dst + US.v len) `Seq.equal`
Seq.slice s0 (US.v idx_src) (US.v idx_src + US.v len) /\
Seq.slice s1' 0 (US.v idx_dst) `Seq.equal`
Seq.slice s1 0 (US.v idx_dst) /\
Seq.slice s1' (US.v idx_dst + US.v len) (length dst) `Seq.equal`
Seq.slice s1 (US.v idx_dst + US.v len) (length dst)
[@@noextract_to "krml"] // primitive
val blit_ptr (#t:_) (#p0:perm) (#s0 #s1:Ghost.erased (Seq.seq t))
(src:ptr t)
(len_src: Ghost.erased nat { offset src + len_src <= base_len (base src) })
(idx_src: US.t)
(dst:ptr t)
(len_dst: Ghost.erased nat { offset dst + len_dst <= base_len (base dst) })
(idx_dst: US.t)
(len: US.t)
: ST unit
(pts_to (| src, len_src |) p0 s0 `star` pts_to (| dst, len_dst |) full_perm s1)
(fun _ -> pts_to (| src, len_src |) p0 s0 `star` exists_ (fun s1' ->
pts_to (| dst, len_dst |) full_perm s1' `star`
pure (blit_post s0 s1 (| src, len_src |) idx_src (| dst, len_dst |) idx_dst len s1')
))
(
US.v idx_src + US.v len <= len_src /\
US.v idx_dst + US.v len <= len_dst
)
(fun _ -> True)
inline_for_extraction
[@@noextract_to "krml"]
let blit (#t:_) (#p0:perm) (#s0 #s1:Ghost.erased (Seq.seq t))
(src:array t)
(idx_src: US.t)
(dst:array t)
(idx_dst: US.t)
(len: US.t)
: ST unit
(pts_to src p0 s0 `star` pts_to dst full_perm s1)
(fun _ -> pts_to src p0 s0 `star` exists_ (fun s1' ->
pts_to dst full_perm s1' `star`
pure (blit_post s0 s1 src idx_src dst idx_dst len s1')
))
(
US.v idx_src + US.v len <= length src /\
US.v idx_dst + US.v len <= length dst
)
(fun _ -> True)
= let (| p_src, len_src |) = src in
vpattern_rewrite #_ #_ #src (fun src -> pts_to src p0 _) (| p_src, len_src |);
let (| p_dst, len_dst |) = dst in
vpattern_rewrite #_ #_ #dst (fun dst -> pts_to dst full_perm _) (| p_dst, len_dst |);
blit_ptr p_src len_src idx_src p_dst len_dst idx_dst len;
let _ = elim_exists () in
elim_pure _;
vpattern_rewrite #_ #_ #(| p_src, _ |) (fun src -> pts_to src p0 _) src;
vpattern_rewrite #_ #_ #(| p_dst, _ |) (fun dst -> pts_to dst full_perm _) dst;
noop ()
inline_for_extraction
[@@noextract_to "krml"]
let memcpy (#t:_) (#p0:perm)
(a0 a1:array t)
(#s0 #s1:Ghost.erased (Seq.seq t))
(l:US.t { US.v l == length a0 /\ length a0 == length a1 } )
: STT unit
(pts_to a0 p0 s0 `star` pts_to a1 full_perm s1)
(fun _ -> pts_to a0 p0 s0 `star` pts_to a1 full_perm s0)
= blit #t #p0 #s0 #s1 a0 0sz a1 0sz l;
let s1' = elim_exists () in
elim_pure (blit_post s0 s1 a0 0sz a1 0sz l s1');
vpattern_rewrite (pts_to a1 full_perm) (Ghost.reveal s0);
return ()
/// An introduction function for the fits_u32 predicate.
/// It will be natively extracted to static_assert (UINT32_MAX <= SIZE_MAX) by krml
[@@noextract_to "krml"]
val intro_fits_u32 (_:unit)
: STT (squash (US.fits_u32))
emp (fun _ -> emp)
/// An introduction function for the fits_u64 predicate.
/// It will be natively extracted to static_assert (UINT64_MAX <= SIZE_MAX) by krml
[@@noextract_to "krml"]
val intro_fits_u64 (_:unit)
: STT (squash (US.fits_u64))
emp (fun _ -> emp)
/// Determining whether int32 values fit in a ptrdiff
/// It will be natively extracted to static_assert (INT32_MAX <= PTRDIFF_MAX) by krml
[@@noextract_to "krml"]
val intro_fits_ptrdiff32 (_:unit)
: STT (squash (UP.fits (FStar.Int.max_int 32)))
emp (fun _ -> emp)
/// Determining whether int32 values fit in a ptrdiff
/// It will be natively extracted to static_assert (INT64_MAX <= PTRDIFF_MAX) by krml
[@@noextract_to "krml"]
val intro_fits_ptrdiff64 (_:unit)
: STT (squash (UP.fits (FStar.Int.max_int 64)))
emp (fun _ -> emp)
/// The pointer substraction, returning a ptrdiff_t.
/// Note, this operation is only defined according to the C standard when
/// both pointers belong to the same allocation unit, which is captured
/// by the `base a0 == base a1` precondition, and when the difference between
/// the two pointers is representable as a ptrdiff_t, captured by the `fits`
/// precondition.
[@@noextract_to "krml"] // primitive
val ptrdiff_ptr (#t:_) (#p0 #p1:perm) (#s0 #s1:Ghost.erased (Seq.seq t))
(a0:ptr t)
(len0: Ghost.erased nat { offset a0 + len0 <= base_len (base a0) })
(a1:ptr t)
(len1: Ghost.erased nat { offset a1 + len1 <= base_len (base a1) })
: ST UP.t
(pts_to (| a0, len0 |) p0 s0 `star` pts_to (| a1, len1 |) p1 s1)
(fun _ -> pts_to (| a0, len0 |) p0 s0 `star` pts_to (| a1, len1 |) p1 s1)
(base a0 == base a1 /\ UP.fits (offset a0 - offset a1))
(fun r -> UP.v r == offset a0 - offset a1)
inline_for_extraction | {
"checked_file": "/",
"dependencies": [
"Steel.ST.Util.fsti.checked",
"Steel.FractionalPermission.fst.checked",
"prims.fst.checked",
"FStar.SizeT.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.PtrdiffT.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Int.fsti.checked",
"FStar.Ghost.fsti.checked"
],
"interface_file": false,
"source_file": "Steel.ST.HigherArray.fsti"
} | [
{
"abbrev": false,
"full_module": "Steel.ST.Util",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.PtrdiffT",
"short_module": "UP"
},
{
"abbrev": true,
"full_module": "FStar.SizeT",
"short_module": "US"
},
{
"abbrev": true,
"full_module": "Steel.FractionalPermission",
"short_module": "P"
},
{
"abbrev": false,
"full_module": "Steel.ST",
"short_module": null
},
{
"abbrev": false,
"full_module": "Steel.ST",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a0: Steel.ST.HigherArray.array t -> a1: Steel.ST.HigherArray.array t
-> Steel.ST.Effect.ST FStar.PtrdiffT.t | Steel.ST.Effect.ST | [] | [] | [
"Steel.FractionalPermission.perm",
"FStar.Ghost.erased",
"FStar.Seq.Base.seq",
"Steel.ST.HigherArray.array",
"Steel.ST.HigherArray.ptr",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"Steel.ST.HigherArray.offset",
"FStar.Ghost.reveal",
"Steel.ST.HigherArray.base_len",
"Steel.ST.HigherArray.base",
"Steel.ST.Util.return",
"FStar.PtrdiffT.t",
"FStar.Ghost.hide",
"FStar.Set.set",
"Steel.Memory.iname",
"FStar.Set.empty",
"Steel.Effect.Common.VStar",
"Steel.ST.HigherArray.pts_to",
"Steel.Effect.Common.vprop",
"Prims.unit",
"Steel.ST.Util.rewrite",
"Prims.Mkdtuple2",
"Steel.ST.HigherArray.ptrdiff_ptr",
"Steel.Effect.Common.star",
"Prims.l_and",
"Prims.eq2",
"Steel.ST.HigherArray.base_t",
"Steel.ST.HigherArray.ptr_of",
"FStar.PtrdiffT.fits",
"Prims.op_Subtraction",
"Prims.l_True",
"Prims.int",
"FStar.PtrdiffT.v"
] | [] | false | true | false | false | false | let ptrdiff (#t: _) (#p0 #p1: perm) (#s0 #s1: Ghost.erased (Seq.seq t)) (a0 a1: array t)
: ST UP.t
((pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(fun _ -> (pts_to a0 p0 s0) `star` (pts_to a1 p1 s1))
(base (ptr_of a0) == base (ptr_of a1) /\ UP.fits (offset (ptr_of a0) - offset (ptr_of a1)))
(fun r -> UP.v r == offset (ptr_of a0) - offset (ptr_of a1)) =
| let (| pt0 , len0 |) = a0 in
let (| pt1 , len1 |) = a1 in
rewrite (pts_to a0 _ _) (pts_to (| pt0, len0 |) p0 s0);
rewrite (pts_to a1 _ _) (pts_to (| pt1, len1 |) p1 s1);
let res = ptrdiff_ptr pt0 len0 pt1 len1 in
rewrite (pts_to (| pt0, len0 |) p0 s0) (pts_to a0 _ _);
rewrite (pts_to (| pt1, len1 |) p1 s1) (pts_to a1 _ _);
return res | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.multiple_modulo_lemma | val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0) | val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0) | let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 62,
"end_line": 568,
"start_col": 0,
"start_line": 568
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> FStar.Pervasives.Lemma (ensures a * n % n = 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.cancel_mul_mod",
"Prims.unit"
] | [] | true | false | true | false | false | let multiple_modulo_lemma (a: int) (n: pos) =
| cancel_mul_mod a n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.multiple_division_lemma | val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a) | val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a) | let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 68,
"end_line": 564,
"start_col": 0,
"start_line": 564
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.nonzero -> FStar.Pervasives.Lemma (ensures a * n / n = a) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nonzero",
"FStar.Math.Lemmas.cancel_mul_div",
"Prims.unit"
] | [] | true | false | true | false | false | let multiple_division_lemma (a: int) (n: nonzero) =
| cancel_mul_div a n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_sub_lemma | val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b) | val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b) | let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 25,
"end_line": 608,
"start_col": 0,
"start_line": 606
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> b: Prims.nat
-> FStar.Pervasives.Lemma (ensures (a - b * n) / n = a / n - b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.nat",
"FStar.Math.Lemmas.lemma_div_plus",
"Prims.op_Minus",
"Prims.unit",
"FStar.Math.Lemmas.neg_mul_left"
] | [] | true | false | true | false | false | let division_sub_lemma (a: int) (n: pos) (b: nat) =
| neg_mul_left b n;
lemma_div_plus a (- b) n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_definition | val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b) | val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b) | let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 560,
"start_col": 0,
"start_line": 558
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> m: Prims.int{a - b < m * b && m * b <= a}
-> FStar.Pervasives.Lemma (ensures m = a / b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.b2t",
"Prims.op_AmpAmp",
"Prims.op_LessThan",
"Prims.op_Subtraction",
"FStar.Mul.op_Star",
"Prims.op_LessThanOrEqual",
"FStar.Math.Lemmas.division_definition_lemma_2",
"Prims.unit",
"FStar.Math.Lemmas.division_definition_lemma_1"
] | [] | true | false | true | false | false | let division_definition a b m =
| division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wp_Poly1305_impl | val va_wp_Poly1305_impl
(key_r key_s: nat128)
(ctx_b inp_b: buffer64)
(finish: nat64)
(va_s0: va_state)
(va_k: (va_state -> int -> Type0))
: Type0 | val va_wp_Poly1305_impl
(key_r key_s: nat128)
(ctx_b inp_b: buffer64)
(finish: nat64)
(va_s0: va_state)
(va_k: (va_state -> int -> Type0))
: Type0 | let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h)))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 34,
"end_line": 2703,
"start_col": 0,
"start_line": 2661
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
key_r: Vale.X64.Machine_s.nat128 ->
key_s: Vale.X64.Machine_s.nat128 ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64 ->
finish: Vale.X64.Memory.nat64 ->
va_s0: Vale.X64.Decls.va_state ->
va_k: (_: Vale.X64.Decls.va_state -> _: Prims.int -> Type0)
-> Type0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Machine_s.nat128",
"Vale.X64.Memory.buffer64",
"Vale.X64.Memory.nat64",
"Vale.X64.Decls.va_state",
"Prims.int",
"Prims.l_and",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Vale.X64.Decls.validDstAddrs64",
"Vale.X64.Decls.va_get_mem_heaplet",
"Vale.X64.Decls.va_get_reg64",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Decls.va_get_mem_layout",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.Decls.validSrcAddrs64",
"Vale.X64.Machine_s.rRsi",
"Vale.Poly1305.Util.readable_words",
"Vale.X64.Machine_s.rRdx",
"Prims.op_LessThan",
"Prims.op_Addition",
"Vale.X64.Machine_s.pow2_64",
"Prims.eq2",
"Vale.Def.Words_s.nat64",
"Vale.X64.Decls.buffer64_read",
"Vale.Def.Words_s.nat128",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.X64.Decls.va_int_range",
"Prims.l_Forall",
"Vale.X64.InsBasic.vale_heap",
"Vale.X64.Flags.t",
"Prims.l_imp",
"Vale.X64.Decls.modifies_buffer_specific",
"Vale.Poly1305.Math.lowerUpper192",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Vale.Poly1305.Spec_s.modp",
"Vale.Poly1305.Spec_s.poly1305_hash_blocks",
"Vale.X64.Decls.va_mul_nat",
"Vale.Poly1305.Spec_s.make_r",
"Prims.op_Division",
"Vale.Poly1305.Spec_s.poly1305_hash_all",
"Vale.Def.Types_s.nat64",
"Vale.Poly1305.Util.t_seqTo128",
"Vale.Poly1305.Util.seqTo128",
"Vale.X64.Decls.buffer64_as_seq",
"Vale.X64.State.vale_state",
"Vale.X64.Decls.va_upd_mem_heaplet",
"Vale.X64.Decls.va_upd_flags",
"Vale.X64.Decls.va_upd_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Decls.va_upd_mem"
] | [] | false | false | false | true | true | let va_wp_Poly1305_impl
(key_r key_s: nat128)
(ctx_b inp_b: buffer64)
(finish: nat64)
(va_s0: va_state)
(va_k: (va_state -> int -> Type0))
: Type0 =
| (va_get_ok va_s0 /\
(let n:(va_int_range 18446744073709551616 18446744073709551616) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0)
ctx_b
24
(va_get_mem_layout va_s0)
Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0)
inp_b
(Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0)
Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in
let key_r1 = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in
let key_s0 = Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in
let key_s1 = Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in
finish == Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\
key_r == Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\
key_s == Vale.Poly1305.Math.lowerUpper128 key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\
(forall (va_x_mem: vale_heap) (va_x_rax: nat64) (va_x_rcx: nat64) (va_x_rdx: nat64)
(va_x_rdi: nat64) (va_x_rsi: nat64) (va_x_rbx: nat64) (va_x_rbp: nat64) (va_x_r8: nat64)
(va_x_r9: nat64) (va_x_r10: nat64) (va_x_r11: nat64) (va_x_r12: nat64) (va_x_r13: nat64)
(va_x_r14: nat64) (va_x_r15: nat64) (va_x_efl: Vale.X64.Flags.t) (va_x_heap1: vale_heap)
(h: int).
let va_sM =
va_upd_mem_heaplet 1
va_x_heap1
(va_upd_flags va_x_efl
(va_upd_reg64 rR15
va_x_r15
(va_upd_reg64 rR14
va_x_r14
(va_upd_reg64 rR13
va_x_r13
(va_upd_reg64 rR12
va_x_r12
(va_upd_reg64 rR11
va_x_r11
(va_upd_reg64 rR10
va_x_r10
(va_upd_reg64 rR9
va_x_r9
(va_upd_reg64 rR8
va_x_r8
(va_upd_reg64 rRbp
va_x_rbp
(va_upd_reg64 rRbx
va_x_rbx
(va_upd_reg64 rRsi
va_x_rsi
(va_upd_reg64 rRdi
va_x_rdi
(va_upd_reg64 rRdx
va_x_rdx
(va_upd_reg64 rRcx
va_x_rcx
(va_upd_reg64 rRax
va_x_rax
(va_upd_mem va_x_mem va_s0
)))))))))))))))))
in
va_get_ok va_sM /\
(let n:(va_int_range 18446744073709551616 18446744073709551616) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM)
ctx_b
24
(va_get_mem_layout va_sM)
Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM)
0
8 /\
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in
let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in
let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in
in
let inp_mem =
Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
inp_b)
in
(finish == 0 ==>
h ==
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_sM)
(va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\
(finish == 0 ==>
Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in)
(va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r)
inp_mem
((va_get_reg64 rRdx va_s0) `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\
(finish == 1 ==>
h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==>
h ==
Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r
key_s
inp_mem
(va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)) ==>
va_k va_sM ((h)))) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_addition_lemma | val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n) | val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n) | let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 72,
"end_line": 625,
"start_col": 0,
"start_line": 625
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> b: Prims.int
-> FStar.Pervasives.Lemma (ensures (a + b * n) % n = a % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.unit"
] | [] | true | false | true | false | false | let modulo_addition_lemma (a: int) (n: pos) (b: int) =
| lemma_mod_plus a b n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_distributivity | val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c) | val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c) | let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 584,
"start_col": 0,
"start_line": 577
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + b) % c == (a % c + b % c) % c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Addition",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_plus_distr_l",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r"
] | [] | false | false | true | false | false | let modulo_distributivity a b c =
| calc ( == ) {
(a + b) % c;
( == ) { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
( == ) { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_plus_mul_distr | val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p) | val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p) | let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 621,
"start_col": 0,
"start_line": 612
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> c: Prims.int -> p: Prims.pos
-> FStar.Pervasives.Lemma (ensures (a + b) * c % p = ((a % p + b % p) % p) * (c % p) % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.op_Addition",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_mod_mul_distr_l",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.modulo_distributivity"
] | [] | false | false | true | false | false | let lemma_mod_plus_mul_distr a b c p =
| calc ( == ) {
((a + b) * c) % p;
( == ) { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
( == ) { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
( == ) { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_sub | val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n) | val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n) | let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 25,
"end_line": 631,
"start_col": 0,
"start_line": 629
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> b: Prims.int
-> FStar.Pervasives.Lemma (ensures (a - b * n) % n = a % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_plus",
"Prims.op_Minus",
"Prims.unit",
"FStar.Math.Lemmas.neg_mul_left"
] | [] | true | false | true | false | false | let lemma_mod_sub (a: int) (n: pos) (b: int) =
| neg_mul_left b n;
lemma_mod_plus a (- b) n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_addition_lemma | val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n ) | val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n ) | let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 81,
"end_line": 573,
"start_col": 0,
"start_line": 573
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> n: Prims.int
-> FStar.Pervasives.Lemma (ensures (a + n * b) / b = a / b + n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.division_definition",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.op_Division",
"Prims.unit"
] | [] | true | false | true | false | false | let division_addition_lemma a b n =
| division_definition (a + n * b) b (a / b + n) | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_qcode_Poly1305_last_block | val va_qcode_Poly1305_last_block (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_last_block ())) | val va_qcode_Poly1305_last_block (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_last_block ())) | let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (())))))))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 46,
"end_line": 1895,
"start_col": 0,
"start_line": 1734
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ()))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | va_mods: Vale.X64.QuickCode.va_mods_t
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305_last_block ()) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCode.va_mods_t",
"Vale.X64.QuickCodes.qblock",
"Prims.unit",
"Prims.Cons",
"Vale.X64.Decls.va_code",
"Vale.X64.Machine_s.IfElse",
"Vale.X64.Decls.ins",
"Vale.X64.Decls.ocmp",
"Vale.X64.QuickCodes.cmp_to_ocmp",
"Vale.X64.QuickCodes.Cmp_lt",
"Vale.X64.Decls.va_op_cmp_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Decls.va_const_cmp",
"Vale.X64.QuickCodes.block",
"Vale.X64.InsBasic.va_code_Mov64",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.InsBasic.va_code_Shl64",
"Vale.X64.Decls.va_const_shift_amt64",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Decls.va_const_opr64",
"Vale.X64.Decls.va_op_shift_amt64_reg64",
"Vale.X64.InsBasic.va_code_Sub64",
"Vale.X64.InsBasic.va_code_And64",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rR9",
"Vale.X64.InsBasic.va_code_Add64Wrap",
"Vale.X64.Machine_s.rR14",
"Vale.X64.InsBasic.va_code_Adc64Wrap",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Prims.Nil",
"Vale.X64.Machine_s.precode",
"Vale.X64.Machine_s.Block",
"Vale.Poly1305.X64.va_code_Poly1305_iteration",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.va_QBind",
"Vale.X64.QuickCodes.va_range1",
"Vale.X64.QuickCodes.va_qIf",
"Vale.X64.QuickCodes.va_qPURE",
"Prims.pure_post",
"Prims.l_and",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.l_Forall",
"Prims.l_imp",
"Vale.Def.Types_s.ishl",
"Prims.eq2",
"Prims.int",
"Prims.op_Multiply",
"Prims.l_or",
"Prims.op_GreaterThanOrEqual",
"Prims.op_GreaterThan",
"Prims.pow2",
"Vale.Poly1305.Math.lemma_bytes_shift_power2",
"Vale.X64.QuickCodes.va_QSeq",
"Vale.X64.InsBasic.va_quick_Mov64",
"Vale.X64.InsBasic.va_quick_Shl64",
"Vale.X64.QuickCodes.va_qAssert",
"Vale.Def.Words_s.pow2_64",
"Vale.X64.Decls.va_get_reg64",
"Prims.op_disEquality",
"Vale.Def.Types_s.iand",
"Prims.op_Subtraction",
"Prims.op_Modulus",
"Vale.Poly1305.Math.lemma_bytes_and_mod",
"Vale.Poly1305.Math.shift_left64",
"Prims.op_LessThanOrEqual",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.Poly1305.Math.lemma_mod_power2_lo",
"Vale.X64.InsBasic.va_quick_Sub64",
"Vale.X64.InsBasic.va_quick_And64",
"Vale.X64.InsBasic.va_quick_Add64Wrap",
"Vale.X64.InsBasic.va_quick_Adc64Wrap",
"Vale.X64.QuickCodes.va_QEmpty",
"Vale.X64.QuickCodes.quickCodes",
"Vale.Def.Words_s.nat64",
"Vale.X64.QuickCodes.va_qAssertSquash",
"Prims.squash",
"Vale.X64.QuickCodes.va_qAssertBy",
"Vale.Def.Words_s.pow2_128",
"Prims.l_True",
"Prims.op_Addition",
"Vale.Poly1305.Math.lemma_power2_add64",
"Vale.Def.Words_s.nat128",
"Vale.Poly1305.Math.lowerUpper128_def",
"Vale.Poly1305.Math.lowerUpper128_reveal",
"Prims.nat",
"Vale.Poly1305.Math.lemma_mod_hi",
"Vale.Def.Words_s.nat8",
"Vale.X64.Decls.va_mul_nat",
"Vale.Poly1305.Math.lowerUpper192",
"Vale.Poly1305.Math.lowerUpper192_def",
"Vale.Poly1305.Math.lowerUpper192_reveal",
"Vale.X64.Machine_s.rR11",
"Vale.Poly1305.X64.va_quick_Poly1305_iteration",
"Vale.Poly1305.Math.lemma_poly_demod",
"Vale.Poly1305.Spec_s.modp",
"Vale.X64.QuickCodes.va_QLemma",
"Vale.X64.Decls.va_reveal_eq",
"Vale.X64.Decls.va_reveal_opaque",
"Prims.pos",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Decls.va_int_range",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCode.va_quickCode",
"Vale.Poly1305.X64.va_code_Poly1305_last_block"
] | [] | false | false | false | false | false | let va_qcode_Poly1305_last_block (va_mods: va_mods_t)
: (va_quickCode unit (va_code_Poly1305_last_block ())) =
| (qblock va_mods
(fun (va_s: va_state) ->
let va_old_s:va_state = va_s in
let n:(va_int_range 18446744073709551616 18446744073709551616) = 18446744073709551616 in
let p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) =
(va_mul_nat n n) `op_Multiply` 4 - 5
in
let r1:nat64 = va_get_reg64 rRax va_s in
let r:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1
in
let hBlocks:Prims.int =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s
)
(va_get_reg64 rRbx va_s))
(va_get_reg64 rRbp va_s)
in
let inpLast:Vale.Def.Words_s.nat128 =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s)
in
let padLast:Prims.pos = Prims.pow2 ((va_get_reg64 rR15 va_s) `op_Multiply` 8) in
va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods
(Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8))
(qblock va_mods
(fun (va_s: va_state) ->
let va_arg78:Vale.Def.Types_s.nat64 = va_get_reg64 rR15 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx))
(fun (va_s: va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast)
(let va_arg77:Vale.Def.Types_s.nat64 =
va_get_reg64 rR15 va_s
in
let va_arg76:Vale.Def.Types_s.nat64 =
va_get_reg64 rR8 va_s
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76
va_arg77)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast ==
Vale.Poly1305.Math.shift_left64 1
(Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15
va_s)
3))
(let va_arg75:Prims.int =
Prims.pow2 ((va_get_reg64 rR15 va_s)
`op_Multiply`
8)
in
let va_arg74:Prims.int =
va_get_reg64 rR15 va_s
in
let va_arg73:Vale.Def.Types_s.nat64 =
va_get_reg64 rR9 va_s
in
let va_arg72:Vale.Def.Types_s.nat64 =
va_get_reg64 rR8 va_s
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_mod_power2_lo
va_arg72
va_arg73
va_arg74
va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64
rRcx)
(va_op_opr64_reg64 rRdx))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64
rRcx)
(va_const_opr64 1))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64
rR8)
(va_op_opr64_reg64 rRcx))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64
rR9)
(va_const_opr64 0))
(fun (va_s: va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8
va_s ==
(va_get_reg64 rR8
va_old_s)
`op_Modulus`
padLast)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128
(va_get_reg64
rR8
va_s)
(va_get_reg64
rR9
va_s) ==
inpLast
`op_Modulus`
padLast)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap
(va_op_dst_opr64_reg64
rR14
)
(va_op_opr64_reg64
rR8)
)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap
(va_op_dst_opr64_reg64
rRbx
)
(va_op_opr64_reg64
rR9
))
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbp
)
(
va_const_opr64
0
)
)
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Add64Wrap
(
va_op_dst_opr64_reg64
rR14
)
(
va_op_opr64_reg64
rRdx
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbx
)
(
va_const_opr64
0
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbp
)
(
va_const_opr64
0
)
)
(
va_QEmpty
(
()
)
)
)
)
))
))))))))))))
))))))
(qblock va_mods
(fun (va_s: va_state) ->
va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255)
(fun _ ->
let nExtra8:nat8 = va_get_reg64 rR15 va_s - 8 in
let va_arg85:Vale.Def.Types_s.nat64 = nExtra8 in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85
)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx)
(va_const_opr64 8))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx))
(fun (va_s: va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast ==
Vale.Poly1305.Math.lowerUpper128 0
(va_get_reg64 rRdx va_s))
(let va_arg84:Prims.nat =
8 `op_Multiply` nExtra8
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_power2_add64
va_arg84)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lowerUpper128_reveal
())
(va_QEmpty (()))))
(let va_arg83:Vale.Def.Types_s.nat64 =
nExtra8
in
let va_arg82:Vale.Def.Types_s.nat64 =
va_get_reg64 rR9 va_s
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_bytes_and_mod
va_arg82
va_arg83)
(va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8
) >=
0 /\
Prims.pow2 (8
`op_Multiply`
nExtra8) <=
18446744073709551615)
(fun _ ->
let va_arg81:Vale.Def.Types_s.nat64
=
Prims.pow2 (8
`op_Multiply`
nExtra8)
in
let va_arg80:Vale.Def.Types_s.nat64
=
va_get_reg64 rR9 va_s
in
let va_arg79:Vale.Def.Types_s.nat64
=
va_get_reg64 rR8 va_s
in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_mod_hi
va_arg79
va_arg80
va_arg81)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64
rRcx)
(va_op_opr64_reg64 rRdx
))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64
rRcx)
(va_const_opr64 1)
)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64
rR9)
(va_op_opr64_reg64
rRcx))
(fun
(va_s:
va_state)
_
->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128
(va_get_reg64
rR8
va_s
)
(va_get_reg64
rR9
va_s
) ==
inpLast
`op_Modulus`
padLast)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap
(va_op_dst_opr64_reg64
rR14
)
(va_op_opr64_reg64
rR8
))
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbx
)
(
va_op_opr64_reg64
rR9
)
)
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbp
)
(
va_const_opr64
0
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Add64Wrap
(
va_op_dst_opr64_reg64
rR14
)
(
va_const_opr64
0
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbx
)
(
va_op_opr64_reg64
rRdx
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Adc64Wrap
(
va_op_dst_opr64_reg64
rRbp
)
(
va_const_opr64
0
)
)
(
va_QEmpty
(
()
)
)
)
)
)
))
))))))))))))
))))))
(fun (va_s: va_state) va_g ->
let h:int = hBlocks + inpLast `op_Modulus` padLast + padLast in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h ==
va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) +
va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ())
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ())
(va_QEmpty (()))))
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ())
(va_QEmpty (())))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1)
(fun (va_s: va_state) (hLast: int) ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast ==
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14
va_s)
(va_get_reg64 rRbx va_s))
(va_get_reg64 rRbp va_s))
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ())
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ())
(va_QEmpty (()))))
(let va_arg71:Prims.int = r in
let va_arg70:Prims.int = inpLast `op_Modulus` padLast + padLast in
let va_arg69:Prims.pos = p in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_: unit) ->
Vale.Poly1305.Math.lemma_poly_demod va_arg69
hBlocks
va_arg70
va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast ==
Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp hBlocks
+
padLast +
inpLast
`op_Modulus`
padLast)
`op_Multiply`
r))
(va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true
(fun _ -> va_reveal_eq (`%modp) modp modp)
(fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))
(va_QEmpty (())))))))))) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_multiplication_division_lemma_2 | val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c)) | val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c)) | let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 36,
"end_line": 827,
"start_col": 0,
"start_line": 824
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c <= b}
-> FStar.Pervasives.Lemma (ensures a * Prims.pow2 c / Prims.pow2 b = a / Prims.pow2 (b - c)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Math.Lemmas.multiple_division_lemma",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.division_multiplication_lemma",
"FStar.Mul.op_Star",
"Prims.op_Subtraction",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_multiplication_division_lemma_2 a b c =
| pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.mod_mul_div_exact | val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0) | val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0) | let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 665,
"start_col": 0,
"start_line": 654
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> n: Prims.pos
-> FStar.Pervasives.Lemma (requires a % (b * n) == 0) (ensures a / b % n == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Division",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Mul.op_Star",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.cancel_mul_div",
"FStar.Math.Lemmas.cancel_mul_mod"
] | [] | false | false | true | false | false | let mod_mul_div_exact (a: int) (b n: pos) =
| calc ( == ) {
(a / b) % n;
( == ) { lemma_div_mod a (b * n) }
(((b * n) * (a / (b * n))) / b) % n;
( == ) { paren_mul_right b n (a / (b * n)) }
((b * (n * (a / (b * n)))) / b) % n;
( == ) { cancel_mul_div (n * (a / (b * n))) b }
(n * (a / (b * n))) % n;
( == ) { cancel_mul_mod (a / (b * n)) n }
0;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.cancel_fraction | val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b) | val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b) | let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 735,
"start_col": 8,
"start_line": 726
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
} | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a * c / (b * c) == a / b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Division",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.division_multiplication_lemma",
"FStar.Math.Lemmas.cancel_mul_div"
] | [] | false | false | true | false | false | let cancel_fraction a b c =
| calc ( == ) {
(a * c) / (b * c);
( == ) { swap_mul b c }
(a * c) / (c * b);
( == ) { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
( == ) { cancel_mul_div a c }
a / b;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_lt_cancel | val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n)) | val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n)) | let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 5,
"end_line": 693,
"start_col": 8,
"start_line": 682
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> n: Prims.int
-> FStar.Pervasives.Lemma (requires a < b * n) (ensures a / b < n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.op_GreaterThanOrEqual",
"Prims.op_Division",
"Prims._assert",
"Prims.l_False",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.b2t",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lib.slash_decr_axiom",
"Prims.squash",
"Prims.bool"
] | [] | false | false | true | false | false | let lemma_div_lt_cancel a b n =
| if a / b >= n
then
(calc ( >= ) {
a;
( >= ) { slash_decr_axiom a b }
(a / b) * b;
( >= ) { () }
n * b;
};
assert False) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_mult_zero | val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0) | val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0) | let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
() | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 4,
"end_line": 705,
"start_col": 8,
"start_line": 696
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a % (b * c) / b / c == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"Prims.unit",
"FStar.Math.Lemmas.nat_over_pos_is_nat",
"Prims.op_Division",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"FStar.Math.Lemmas.lemma_div_lt_cancel",
"FStar.Math.Lemmas.lemma_mod_lt"
] | [] | true | false | true | false | false | let lemma_mod_mult_zero a b c =
| lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
() | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_modulo_modulo_lemma_1 | val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b ) | val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b ) | let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b)) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 47,
"end_line": 867,
"start_col": 0,
"start_line": 865
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c >= b}
-> FStar.Pervasives.Lemma (ensures a % Prims.pow2 c % Prims.pow2 b = a % Prims.pow2 b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lemmas.modulo_modulo_lemma",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_modulo_modulo_lemma_1 a b c =
| pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b)) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_multiplication_division_lemma_1 | val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b)) | val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b)) | let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 53,
"end_line": 820,
"start_col": 0,
"start_line": 816
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c >= b}
-> FStar.Pervasives.Lemma (ensures a * Prims.pow2 c / Prims.pow2 b = a * Prims.pow2 (c - b)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lemmas.multiple_division_lemma",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.paren_mul_left",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_multiplication_division_lemma_1 a b c =
| pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_modulo_modulo_lemma_2 | val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c ) | val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c ) | let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 44,
"end_line": 873,
"start_col": 0,
"start_line": 871
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c <= b}
-> FStar.Pervasives.Lemma (ensures a % Prims.pow2 c % Prims.pow2 b = a % Prims.pow2 c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Math.Lemmas.small_modulo_lemma_1",
"Prims.op_Modulus",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_le_compat"
] | [] | true | false | true | false | false | let pow2_modulo_modulo_lemma_2 a b c =
| pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_scale_lemma | val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b) | val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b) | let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 751,
"start_col": 0,
"start_line": 738
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
} | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a * b % (b * c) == (a % c) * b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Subtraction",
"Prims.op_Division",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.cancel_fraction",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.distributivity_sub_left",
"FStar.Math.Lemmas.swap_mul"
] | [] | false | false | true | false | false | let modulo_scale_lemma a b c =
| calc ( == ) {
(a * b) % (b * c);
( == ) { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
( == ) { cancel_fraction a c b }
a * b - (b * c) * (a / c);
( == ) { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
( == ) { (swap_mul b (c * (a / c));
distributivity_sub_left a (c * (a / c)) b) }
(a - c * (a / c)) * b;
( == ) { lemma_div_mod a c }
(a % c) * b;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_modulo_division_lemma_2 | val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 ) | val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 ) | let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 46,
"end_line": 861,
"start_col": 0,
"start_line": 859
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c <= b}
-> FStar.Pervasives.Lemma (ensures a % Prims.pow2 c / Prims.pow2 b = 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Math.Lemmas.small_division_lemma_1",
"Prims.op_Modulus",
"Prims.pow2",
"Prims.unit",
"FStar.Math.Lemmas.pow2_le_compat"
] | [] | true | false | true | false | false | let pow2_modulo_division_lemma_2 a b c =
| pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_division_lemma_0 | val modulo_division_lemma_0 (a: nat) (b c: pos)
: Lemma (a / (b * c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c)) | val modulo_division_lemma_0 (a: nat) (b c: pos)
: Lemma (a / (b * c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c)) | let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
() | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 6,
"end_line": 769,
"start_col": 0,
"start_line": 756
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = () | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.nat -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma
(ensures a / (b * c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - (a / (b * c)) * c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.pos",
"Prims.unit",
"FStar.Math.Lemmas.division_sub_lemma",
"FStar.Mul.op_Star",
"Prims.op_Division",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.cut",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.swap_mul",
"Prims.squash",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lib.slash_decr_axiom",
"Prims.l_True",
"Prims.l_and",
"Prims.op_LessThanOrEqual",
"Prims.op_Subtraction",
"FStar.Pervasives.pattern"
] | [] | false | false | true | false | false | let modulo_division_lemma_0 (a: nat) (b c: pos)
: Lemma (a / (b * c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c)) =
| slash_decr_axiom a (b * c);
calc ( == ) {
(a / (b * c)) * (b * c);
( == ) { swap_mul b c }
(a / (b * c)) * (c * b);
( == ) { paren_mul_right (a / (b * c)) c b }
((a / (b * c)) * c) * b;
};
cut ((a / (b * c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b * c);
division_sub_lemma a b ((a / (b * c)) * c);
() | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_2 | val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c ) | val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c ) | let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 849,
"start_col": 0,
"start_line": 840
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c ) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c <= b}
-> FStar.Pervasives.Lemma
(ensures a * Prims.pow2 c % Prims.pow2 b = (a % Prims.pow2 (b - c)) * Prims.pow2 c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"FStar.Math.Lemmas.pow2_plus",
"FStar.Math.Lemmas.modulo_scale_lemma"
] | [] | false | false | true | false | false | let pow2_multiplication_modulo_lemma_2 a b c =
| calc ( == ) {
(a * pow2 c) % pow2 b;
( == ) { () }
(a * pow2 c) % pow2 (c + (b - c));
( == ) { pow2_plus c (b - c) }
(a * pow2 c) % (pow2 c * pow2 (b - c));
( == ) { modulo_scale_lemma a (pow2 c) (pow2 (b - c)) }
(a % pow2 (b - c)) * pow2 c;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_plus_injective | val lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) : Lemma
(requires b < n /\ c < n /\ (a + b) % n = (a + c) % n)
(ensures b = c) | val lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) : Lemma
(requires b < n /\ c < n /\ (a + b) % n = (a + c) % n)
(ensures b = c) | let lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) =
small_mod b n;
small_mod c n;
mod_add_both (a + b) (a + c) (-a) n | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 37,
"end_line": 912,
"start_col": 0,
"start_line": 909
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p))
let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p
val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p)
let lemma_mod_twice a p = lemma_mod_mod (a % p) a p
val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p))
let modulo_sub p a b c =
modulo_add p (-a) (a + b) (a + c)
val mod_add_both (a:int) (b:int) (x:int) (n:pos) : Lemma
(requires a % n == b % n)
(ensures (a + x) % n == (b + x) % n)
let mod_add_both (a:int) (b:int) (x:int) (n:pos) =
calc (==) {
(a + x) % n;
== { modulo_distributivity a x n }
((a % n) + (x % n)) % n;
== { (* hyp *) }
((b % n) + (x % n)) % n;
== { modulo_distributivity b x n }
(b + x) % n;
}
val lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) : Lemma
(requires b < n /\ c < n /\ (a + b) % n = (a + c) % n) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | n: Prims.pos -> a: Prims.int -> b: Prims.nat -> c: Prims.nat
-> FStar.Pervasives.Lemma (requires b < n /\ c < n /\ (a + b) % n = (a + c) % n) (ensures b = c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"Prims.int",
"Prims.nat",
"FStar.Math.Lemmas.mod_add_both",
"Prims.op_Addition",
"Prims.op_Minus",
"Prims.unit",
"FStar.Math.Lemmas.small_mod"
] | [] | true | false | true | false | false | let lemma_mod_plus_injective (n: pos) (a: int) (b c: nat) =
| small_mod b n;
small_mod c n;
mod_add_both (a + b) (a + c) (- a) n | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.mod_mult_exact | val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0) | val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0) | let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 649,
"start_col": 0,
"start_line": 637
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> n: Prims.pos -> q: Prims.pos
-> FStar.Pervasives.Lemma (requires a % (n * q) == 0) (ensures a % n == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Mul.op_Star",
"Prims.op_Division",
"Prims.op_Addition",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.swap_mul",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.multiple_modulo_lemma"
] | [] | false | false | true | false | false | let mod_mult_exact (a: int) (n q: pos) =
| calc ( == ) {
a % n;
( == ) { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
( == ) { () }
((n * q) * (a / (n * q))) % n;
( == ) { (paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q)))) }
((q * (a / (n * q))) * n) % n;
( == ) { multiple_modulo_lemma (q * (a / (n * q))) n }
0;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_multiplication_modulo_lemma_1 | val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 ) | val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 ) | let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 51,
"end_line": 835,
"start_col": 0,
"start_line": 831
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.nat{c >= b}
-> FStar.Pervasives.Lemma (ensures a * Prims.pow2 c % Prims.pow2 b = 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lemmas.multiple_modulo_lemma",
"FStar.Mul.op_Star",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.paren_mul_left",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_multiplication_modulo_lemma_1 a b c =
| pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.mod_pow2_div2 | val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0) | val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0) | let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1)) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 38,
"end_line": 675,
"start_col": 0,
"start_line": 671
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 1,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> m: Prims.pos
-> FStar.Pervasives.Lemma (requires a % Prims.pow2 m == 0)
(ensures a / 2 % Prims.pow2 (m - 1) == 0) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.mod_mul_div_exact",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.squash",
"Prims.op_Division",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | true | false | true | false | false | let mod_pow2_div2 (a: int) (m: pos)
: Lemma (requires a % pow2 m == 0) (ensures (a / 2) % pow2 (m - 1) == 0) =
| mod_mul_div_exact a 2 (pow2 (m - 1)) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_add | val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p)) | val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p)) | let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 29,
"end_line": 880,
"start_col": 0,
"start_line": 878
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | p: Prims.pos -> a: Prims.int -> b: Prims.int -> c: Prims.int
-> FStar.Pervasives.Lemma (requires b % p = c % p) (ensures (a + b) % p = (a + c) % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"Prims.int",
"FStar.Math.Lemmas.modulo_distributivity",
"Prims.unit"
] | [] | true | false | true | false | false | let modulo_add p a b c =
| modulo_distributivity a b p;
modulo_distributivity a c p | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_mod_twice | val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p) | val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p) | let lemma_mod_twice a p = lemma_mod_mod (a % p) a p | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 51,
"end_line": 883,
"start_col": 0,
"start_line": 883
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p))
let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> p: Prims.pos -> FStar.Pervasives.Lemma (ensures a % p % p == a % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Math.Lemmas.lemma_mod_mod",
"Prims.op_Modulus",
"Prims.unit"
] | [] | true | false | true | false | false | let lemma_mod_twice a p =
| lemma_mod_mod (a % p) a p | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wpProof_Poly1305 | val va_wpProof_Poly1305 : win:bool -> ctx_b:buffer64 -> inp_b:buffer64 -> len_in:nat64 ->
finish_in:nat64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305 win ctx_b inp_b len_in finish_in va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305 win) ([va_Mod_stackTaint;
va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp; va_Mod_reg64 rRbp; va_Mod_reg64 rRdi;
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) | val va_wpProof_Poly1305 : win:bool -> ctx_b:buffer64 -> inp_b:buffer64 -> len_in:nat64 ->
finish_in:nat64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305 win ctx_b inp_b len_in finish_in va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305 win) ([va_Mod_stackTaint;
va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp; va_Mod_reg64 rRbp; va_Mod_reg64 rRdi;
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) | let va_wpProof_Poly1305 win ctx_b inp_b len_in finish_in va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305 (va_code_Poly1305 win) va_s0 win ctx_b inp_b len_in
finish_in in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_stackTaint va_sM (va_update_stack va_sM
(va_update_mem_layout va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRsp va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRsi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem va_sM
va_s0))))))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_stackTaint; va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 1;
va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp;
va_Mod_reg64 rRbp; va_Mod_reg64 rRdi; va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 3015,
"start_col": 0,
"start_line": 2996
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b
inp_b finish in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem
va_sM va_s0))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) : (va_quickCode int (va_code_Poly1305_impl ())) =
(va_QProc (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi;
va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem])
(va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish) (va_wpProof_Poly1305_impl key_r key_s
ctx_b inp_b finish))
//--
//-- Poly1305
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305 win =
(va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRax) (va_op_opr64_reg64 rRdi)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11)
(va_op_opr64_reg64 rRsi)) (va_CCons (if win then va_Block (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_CNil ()))))) else va_Block (va_CNil
())) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRcx) 184 Public) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rRbx)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRbp))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR11)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR12))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR14)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR15))
(va_CCons (va_code_Poly1305_impl ()) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbp) 16
Public) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_CCons
(va_code_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR12))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbp))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_DestroyHeaplets ())
(va_CNil ())))))))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305 win =
(va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi)) (va_pbool_and (if win then va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_ttrue
())))) else va_ttrue ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRcx) 184
Public) (va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Poly1305_impl ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRsi)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbp)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRdi) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue
()))))))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305 (va_mods:va_mods_t) (win:bool) (ctx_b:buffer64) (inp_b:buffer64)
(len_in:nat64) (finish_in:nat64) : (va_quickCode unit (va_code_Poly1305 win)) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(ctx_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)
(fun _ -> va_get_reg64 rRdi va_s) in let (inp_in:(va_int_range 0 18446744073709551615)) = va_if
win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 754 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_CreateHeaplets ([declare_buffer64 inp_b 0 Public Immutable; declare_buffer64 ctx_b 1
Public Mutable])) (fun (va_s:va_state) _ -> let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in let (key_s0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 5
(va_get_mem_heaplet 1 va_s) in let (key_s1:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s) in let
(key_r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 in let
(key_s:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 key_s0 key_s1 in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 764 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 765 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi)) (fun (va_s:va_state) _
-> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 766 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 768 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 769 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 770 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 771 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_QEmpty (())))))))
(qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 785 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRcx) 184 Public ctx_b 23) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 788 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 789 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 790 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 791 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 792 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 793 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 794 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 795 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 797 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_impl key_r key_s ctx_b inp_b finish_in) (fun (va_s:va_state) (h':int) ->
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 799 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 800 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 801 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 804 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 805 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 806 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 807 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR12)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 808 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 809 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 810 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 811 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 813 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 815 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_DestroyHeaplets ()) (va_QEmpty (()))))))))))))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305 va_b0 va_s0 win ctx_b inp_b len_in finish_in =
let (va_mods:va_mods_t) = [va_Mod_stackTaint; va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp;
va_Mod_reg64 rRbp; va_Mod_reg64 rRdi; va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305 va_mods win ctx_b inp_b len_in finish_in in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305 win) va_qc va_s0 (fun va_s0
va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 683 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (ctx_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ ->
va_get_reg64 rRcx va_s0) (fun _ -> va_get_reg64 rRdi va_s0) in let (inp_in:(va_int_range 0
18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRdx va_s0) (fun _ -> va_get_reg64
rRsi va_s0) in let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 718 column 46 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Util.modifies_buffer ctx_b (va_get_mem va_s0) (va_get_mem va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 720 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 721 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 722 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 723 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 724 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_r1 = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 725 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_s0 = Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 726 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_s1 = Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 727 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 728 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_r = Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 in label va_range1
"***** POSTCONDITION NOT MET AT line 729 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let key_s = Vale.Poly1305.Math.lowerUpper128 key_s0 key_s1 in label va_range1
"***** POSTCONDITION NOT MET AT line 731 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_out = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 732 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_out = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 733 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_out = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 734 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h10 = Vale.Poly1305.Math.lowerUpper128 h0_out h1_out in label va_range1
"***** POSTCONDITION NOT MET AT line 735 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h210 = Vale.Poly1305.Math.lowerUpper192 h10 h2_out in label va_range1
"***** POSTCONDITION NOT MET AT line 736 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem va_sM)
inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 739 column 103 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish_in == 0 ==> Vale.Poly1305.Spec_s.modp h210 == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(len_in `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 740 column 38 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish_in == 0 ==> h2_out < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 741 column 95 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish_in == 1 ==> h10 == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp
h_in) key_r key_s inp_mem len_in) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 743 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsp va_sM == va_get_reg64 rRsp va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 745 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(win ==> va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 746 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(win ==> va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 747 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == va_get_reg64 rRbx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 748 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == va_get_reg64 rRbp va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 749 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == va_get_reg64 rR12 va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 750 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR13 va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 751 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == va_get_reg64 rR14 va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 752 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM == va_get_reg64 rR15 va_s0))))))))))))))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_stackTaint; va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 1;
va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp;
va_Mod_reg64 rRbp; va_Mod_reg64 rRdi; va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
(va_sM, va_fM) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
win: Prims.bool ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64 ->
len_in: Vale.X64.Memory.nat64 ->
finish_in: Vale.X64.Memory.nat64 ->
va_s0: Vale.X64.Decls.va_state ->
va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0)
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit) | Prims.Ghost | [] | [] | [
"Prims.bool",
"Vale.X64.Memory.buffer64",
"Vale.X64.Memory.nat64",
"Vale.X64.Decls.va_state",
"Prims.unit",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.Mktuple3",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_stackTaint",
"Vale.X64.QuickCode.va_Mod_stack",
"Vale.X64.QuickCode.va_Mod_mem_layout",
"Vale.X64.QuickCode.va_Mod_mem_heaplet",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRsp",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRax",
"Vale.X64.QuickCode.va_Mod_mem",
"Prims.Nil",
"Prims._assert",
"Vale.X64.Decls.va_state_eq",
"Vale.X64.Decls.va_update_stackTaint",
"Vale.X64.Decls.va_update_stack",
"Vale.X64.Decls.va_update_mem_layout",
"Vale.X64.Decls.va_update_mem_heaplet",
"Vale.X64.Decls.va_update_flags",
"Vale.X64.Decls.va_update_reg64",
"Vale.X64.Decls.va_update_ok",
"Vale.X64.Decls.va_update_mem",
"Vale.X64.Decls.va_lemma_upd_update",
"FStar.Pervasives.Native.tuple3",
"FStar.Pervasives.Native.tuple2",
"Vale.X64.State.vale_state",
"Vale.Poly1305.X64.va_lemma_Poly1305",
"Vale.Poly1305.X64.va_code_Poly1305"
] | [] | false | false | false | false | false | let va_wpProof_Poly1305 win ctx_b inp_b len_in finish_in va_s0 va_k =
| let va_sM, va_f0 =
va_lemma_Poly1305 (va_code_Poly1305 win) va_s0 win ctx_b inp_b len_in finish_in
in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM
(va_update_stackTaint va_sM
(va_update_stack va_sM
(va_update_mem_layout va_sM
(va_update_mem_heaplet 1
va_sM
(va_update_flags va_sM
(va_update_reg64 rR15
va_sM
(va_update_reg64 rR14
va_sM
(va_update_reg64 rR13
va_sM
(va_update_reg64 rR12
va_sM
(va_update_reg64 rR11
va_sM
(va_update_reg64 rR10
va_sM
(va_update_reg64 rR9
va_sM
(va_update_reg64 rR8
va_sM
(va_update_reg64 rRsp
va_sM
(va_update_reg64 rRbp
va_sM
(va_update_reg64 rRdi
va_sM
(va_update_reg64 rRsi
va_sM
(va_update_reg64 rRdx
va_sM
(va_update_reg64 rRcx
va_sM
(va_update_reg64 rRbx
va_sM
(va_update_reg64
rRax
va_sM
(va_update_ok
va_sM
(va_update_mem
va_sM
va_s0
))))
))))))))))))))))))));
va_lemma_norm_mods ([
va_Mod_stackTaint; va_Mod_stack; va_Mod_mem_layout; va_Mod_mem_heaplet 1; va_Mod_flags;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRsp; va_Mod_reg64 rRbp;
va_Mod_reg64 rRdi; va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx;
va_Mod_reg64 rRax; va_Mod_mem
])
va_sM
va_s0;
let va_g = () in
(va_sM, va_f0, va_g) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_sub | val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p)) | val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p)) | let modulo_sub p a b c =
modulo_add p (-a) (a + b) (a + c) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 35,
"end_line": 890,
"start_col": 0,
"start_line": 889
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p))
let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p
val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p)
let lemma_mod_twice a p = lemma_mod_mod (a % p) a p
val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | p: Prims.pos -> a: Prims.int -> b: Prims.int -> c: Prims.int
-> FStar.Pervasives.Lemma (requires (a + b) % p = (a + c) % p) (ensures b % p = c % p) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.pos",
"Prims.int",
"FStar.Math.Lemmas.modulo_add",
"Prims.op_Minus",
"Prims.op_Addition",
"Prims.unit"
] | [] | true | false | true | false | false | let modulo_sub p a b c =
| modulo_add p (- a) (a + b) (a + c) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.mod_add_both | val mod_add_both (a:int) (b:int) (x:int) (n:pos) : Lemma
(requires a % n == b % n)
(ensures (a + x) % n == (b + x) % n) | val mod_add_both (a:int) (b:int) (x:int) (n:pos) : Lemma
(requires a % n == b % n)
(ensures (a + x) % n == (b + x) % n) | let mod_add_both (a:int) (b:int) (x:int) (n:pos) =
calc (==) {
(a + x) % n;
== { modulo_distributivity a x n }
((a % n) + (x % n)) % n;
== { (* hyp *) }
((b % n) + (x % n)) % n;
== { modulo_distributivity b x n }
(b + x) % n;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 904,
"start_col": 0,
"start_line": 895
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p))
let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p
val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p)
let lemma_mod_twice a p = lemma_mod_mod (a % p) a p
val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p))
let modulo_sub p a b c =
modulo_add p (-a) (a + b) (a + c)
val mod_add_both (a:int) (b:int) (x:int) (n:pos) : Lemma
(requires a % n == b % n) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> x: Prims.int -> n: Prims.pos
-> FStar.Pervasives.Lemma (requires a % n == b % n) (ensures (a + x) % n == (b + x) % n) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.op_Addition",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.modulo_distributivity",
"Prims.squash"
] | [] | false | false | true | false | false | let mod_add_both (a b x: int) (n: pos) =
| calc ( == ) {
(a + x) % n;
( == ) { modulo_distributivity a x n }
((a % n) + (x % n)) % n;
( == ) { () }
((b % n) + (x % n)) % n;
( == ) { modulo_distributivity b x n }
(b + x) % n;
} | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.codes | val codes : Type0 | let codes = va_codes | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 27,
"end_line": 15,
"start_col": 7,
"start_line": 15
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | Type0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Decls.va_codes"
] | [] | false | false | false | true | true | let codes =
| va_codes | false |
|
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_wpProof_Poly1305_impl | val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) | val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) | let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b
inp_b finish in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem
va_sM va_s0))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 22,
"end_line": 2732,
"start_col": 0,
"start_line": 2716
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g)))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
key_r: Vale.X64.Machine_s.nat128 ->
key_s: Vale.X64.Machine_s.nat128 ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64 ->
finish: Vale.X64.Memory.nat64 ->
va_s0: Vale.X64.Decls.va_state ->
va_k: (_: Vale.X64.Decls.va_state -> _: Prims.int -> Type0)
-> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.int) | Prims.Ghost | [] | [] | [
"Vale.X64.Machine_s.nat128",
"Vale.X64.Memory.buffer64",
"Vale.X64.Memory.nat64",
"Vale.X64.Decls.va_state",
"Prims.int",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.Mktuple3",
"Prims.unit",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_mem_heaplet",
"Vale.X64.QuickCode.va_Mod_flags",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rR10",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRax",
"Vale.X64.QuickCode.va_Mod_mem",
"Prims.Nil",
"Prims._assert",
"Vale.X64.Decls.va_state_eq",
"Vale.X64.Decls.va_update_mem_heaplet",
"Vale.X64.Decls.va_update_flags",
"Vale.X64.Decls.va_update_reg64",
"Vale.X64.Decls.va_update_ok",
"Vale.X64.Decls.va_update_mem",
"Vale.X64.Decls.va_lemma_upd_update",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.Poly1305.X64.va_lemma_Poly1305_impl",
"Vale.Poly1305.X64.va_code_Poly1305_impl"
] | [] | false | false | false | false | false | let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
| let va_sM, va_f0, h =
va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b inp_b finish
in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM
(va_update_mem_heaplet 1
va_sM
(va_update_flags va_sM
(va_update_reg64 rR15
va_sM
(va_update_reg64 rR14
va_sM
(va_update_reg64 rR13
va_sM
(va_update_reg64 rR12
va_sM
(va_update_reg64 rR11
va_sM
(va_update_reg64 rR10
va_sM
(va_update_reg64 rR9
va_sM
(va_update_reg64 rR8
va_sM
(va_update_reg64 rRbp
va_sM
(va_update_reg64 rRbx
va_sM
(va_update_reg64 rRsi
va_sM
(va_update_reg64 rRdi
va_sM
(va_update_reg64 rRdx
va_sM
(va_update_reg64 rRcx
va_sM
(va_update_reg64 rRax
va_sM
(va_update_ok va_sM
(va_update_mem va_sM
va_s0)))))))))))))
)))))));
va_lemma_norm_mods ([
va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem
])
va_sM
va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g) | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_division_lemma | val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c) | val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c) | let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 787,
"start_col": 0,
"start_line": 774
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.nat -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a % (b * c) / b = a / b % c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.int",
"Prims.eq2",
"Prims.op_Division",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Subtraction",
"Prims.op_Addition",
"Prims.op_Minus",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.neg_mul_right",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.lemma_div_plus",
"FStar.Math.Lemmas.division_multiplication_lemma"
] | [] | false | false | true | false | false | let modulo_division_lemma a b c =
| calc ( == ) {
(a % (b * c)) / b;
( == ) { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
( == ) { (paren_mul_right b c ((a / (b * c)));
neg_mul_right b (c * (a / (b * c)))) }
(a + b * (- (c * (a / (b * c))))) / b;
( == ) { lemma_div_plus a (- (c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
( == ) { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
( == ) { lemma_div_mod (a / b) c }
(a / b) % c;
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.pow2_modulo_division_lemma_1 | val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) ) | val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) ) | let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b)) | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 49,
"end_line": 855,
"start_col": 0,
"start_line": 853
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} -> | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.nat -> b: Prims.nat -> c: Prims.nat{c >= b}
-> FStar.Pervasives.Lemma
(ensures a % Prims.pow2 c / Prims.pow2 b = a / Prims.pow2 b % Prims.pow2 (c - b)) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.nat",
"Prims.b2t",
"Prims.op_GreaterThanOrEqual",
"FStar.Math.Lemmas.modulo_division_lemma",
"Prims.pow2",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Math.Lemmas.pow2_plus"
] | [] | true | false | true | false | false | let pow2_modulo_division_lemma_1 a b c =
| pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b)) | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.eval | val eval : c: Vale.X64.Decls.va_code ->
s0: Vale.X64.Decls.va_state ->
f0: Vale.X64.Decls.va_fuel ->
sN: Vale.X64.Decls.va_state
-> Vale.Def.Prop_s.prop0 | let eval = eval_code | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 27,
"end_line": 17,
"start_col": 7,
"start_line": 17
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
c: Vale.X64.Decls.va_code ->
s0: Vale.X64.Decls.va_state ->
f0: Vale.X64.Decls.va_fuel ->
sN: Vale.X64.Decls.va_state
-> Vale.Def.Prop_s.prop0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Decls.eval_code"
] | [] | false | false | false | true | false | let eval =
| eval_code | false |
|
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_sub_lemma | val modulo_sub_lemma (a : int) (b : nat) (c : pos) :
Lemma
(requires (b < c /\ (a - b) % c = 0))
(ensures (b = a % c)) | val modulo_sub_lemma (a : int) (b : nat) (c : pos) :
Lemma
(requires (b < c /\ (a - b) % c = 0))
(ensures (b = a % c)) | let modulo_sub_lemma a b c =
calc (==) {
b;
== { modulo_lemma b c }
b % c;
== { lemma_mod_twice b c }
(b%c) % c;
== { (* hyp *) }
(b%c + (a-b)%c) % c;
== { modulo_distributivity b (a-b) c }
(b+(a-b)) % c;
== {}
a % c;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 932,
"start_col": 0,
"start_line": 919
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b)
let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
}
val pow2_multiplication_division_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) / pow2 b = a * pow2 (c - b))
let pow2_multiplication_division_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_division_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) / pow2 b = a / pow2 (b - c))
let pow2_multiplication_division_lemma_2 a b c =
pow2_plus c (b - c);
division_multiplication_lemma (a * pow2 c) (pow2 c) (pow2 (b - c));
multiple_division_lemma a (pow2 c)
val pow2_multiplication_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a * pow2 c) % pow2 b = 0 )
let pow2_multiplication_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
paren_mul_right a (pow2 (c - b)) (pow2 b);
paren_mul_left a (pow2 (c - b)) (pow2 b);
multiple_modulo_lemma (a * pow2 (c - b)) (pow2 b)
val pow2_multiplication_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a * pow2 c) % pow2 b = (a % pow2 (b - c)) * pow2 c )
let pow2_multiplication_modulo_lemma_2 a b c =
calc (==) {
(a * pow2 c) % pow2 b;
== {}
(a * pow2 c) % pow2 (c + (b-c));
== { pow2_plus c (b-c) }
(a * pow2 c) % (pow2 c * pow2 (b-c));
== { modulo_scale_lemma a (pow2 c) (pow2 (b-c)) }
(a % pow2 (b - c)) * pow2 c;
}
val pow2_modulo_division_lemma_1: a:nat -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) / pow2 b = (a / pow2 b) % (pow2 (c - b)) )
let pow2_modulo_division_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_division_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_division_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) / pow2 b = 0 )
let pow2_modulo_division_lemma_2 a b c =
pow2_le_compat b c;
small_division_lemma_1 (a % pow2 c) (pow2 b)
val pow2_modulo_modulo_lemma_1: a:int -> b:nat -> c:nat{c >= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 b )
let pow2_modulo_modulo_lemma_1 a b c =
pow2_plus (c - b) b;
modulo_modulo_lemma a (pow2 b) (pow2 (c - b))
val pow2_modulo_modulo_lemma_2: a:int -> b:nat -> c:nat{c <= b} ->
Lemma ( (a % pow2 c) % pow2 b = a % pow2 c )
let pow2_modulo_modulo_lemma_2 a b c =
pow2_le_compat b c;
small_modulo_lemma_1 (a % pow2 c) (pow2 b)
val modulo_add : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires (b % p = c % p))
(ensures ((a + b) % p = (a + c) % p))
let modulo_add p a b c =
modulo_distributivity a b p;
modulo_distributivity a c p
val lemma_mod_twice : a:int -> p:pos -> Lemma ((a % p) % p == a % p)
let lemma_mod_twice a p = lemma_mod_mod (a % p) a p
val modulo_sub : p:pos -> a:int -> b:int -> c:int -> Lemma
(requires ((a + b) % p = (a + c) % p))
(ensures (b % p = c % p))
let modulo_sub p a b c =
modulo_add p (-a) (a + b) (a + c)
val mod_add_both (a:int) (b:int) (x:int) (n:pos) : Lemma
(requires a % n == b % n)
(ensures (a + x) % n == (b + x) % n)
let mod_add_both (a:int) (b:int) (x:int) (n:pos) =
calc (==) {
(a + x) % n;
== { modulo_distributivity a x n }
((a % n) + (x % n)) % n;
== { (* hyp *) }
((b % n) + (x % n)) % n;
== { modulo_distributivity b x n }
(b + x) % n;
}
val lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) : Lemma
(requires b < n /\ c < n /\ (a + b) % n = (a + c) % n)
(ensures b = c)
let lemma_mod_plus_injective (n:pos) (a:int) (b:nat) (c:nat) =
small_mod b n;
small_mod c n;
mod_add_both (a + b) (a + c) (-a) n
(* Another characterization of the modulo *)
val modulo_sub_lemma (a : int) (b : nat) (c : pos) :
Lemma
(requires (b < c /\ (a - b) % c = 0)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.nat -> c: Prims.pos
-> FStar.Pervasives.Lemma (requires b < c /\ (a - b) % c = 0) (ensures b = a % c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.nat",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"Prims.op_Subtraction",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_twice",
"FStar.Math.Lemmas.modulo_distributivity"
] | [] | false | false | true | false | false | let modulo_sub_lemma a b c =
| calc ( == ) {
b;
( == ) { modulo_lemma b c }
b % c;
( == ) { lemma_mod_twice b c }
(b % c) % c;
( == ) { () }
(b % c + (a - b) % c) % c;
( == ) { modulo_distributivity b (a - b) c }
(b + (a - b)) % c;
( == ) { () }
a % c;
} | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.code | val code : Type0 | let code = va_code | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 25,
"end_line": 14,
"start_col": 7,
"start_line": 14
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | Type0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Decls.va_code"
] | [] | false | false | false | true | true | let code =
| va_code | false |
|
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.labeled_wrap | val labeled_wrap (r: range) (msg: string) (p: Type0) : GTot Type0 | val labeled_wrap (r: range) (msg: string) (p: Type0) : GTot Type0 | let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 80,
"end_line": 20,
"start_col": 0,
"start_line": 20
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | r: FStar.Range.range -> msg: Prims.string -> p: Type0 -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"FStar.Range.range",
"Prims.string",
"FStar.Range.labeled"
] | [] | false | false | false | false | true | let labeled_wrap (r: range) (msg: string) (p: Type0) : GTot Type0 =
| labeled r msg p | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.fuel | val fuel : Type0 | let fuel = va_fuel | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 25,
"end_line": 16,
"start_col": 7,
"start_line": 16
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | Type0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.Decls.va_fuel"
] | [] | false | false | false | true | true | let fuel =
| va_fuel | false |
|
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.division_multiplication_lemma | val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c) | val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c) | let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 723,
"start_col": 0,
"start_line": 710
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a / (b * c) = a / b / c) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Division",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"Prims.op_Modulus",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.lemma_div_plus",
"FStar.Math.Lemmas.lemma_mod_mult_zero"
] | [] | false | false | true | false | false | let division_multiplication_lemma (a: int) (b c: pos) =
| calc ( == ) {
a / b / c;
( == ) { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
( == ) { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
( == ) { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
( == ) { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
( == ) { lemma_mod_mult_zero a b c }
a / (b * c);
} | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.modulo_modulo_lemma | val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b) | val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b) | let modulo_modulo_lemma (a:int) (b:pos) (c:pos) =
pos_times_pos_is_pos b c;
calc (==) {
(a % (b * c)) % b;
== { calc (==) {
a % (b * c);
== { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
== { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
}}
(a - b * (c * (a / (b * c)))) % b;
== { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
== { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (-c * (a / (b * c))))) % b;
== { () }
(a + (-c * (a / (b * c))) * b) % b;
== { lemma_mod_plus a (-c * (a / (b * c))) b}
a % b;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 812,
"start_col": 0,
"start_line": 792
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d))
let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
}
(* Lemma: Division distributivity under special condition *)
val division_sub_lemma (a:int) (n:pos) (b:nat) : Lemma ((a - b * n) / n = a / n - b)
let division_sub_lemma (a:int) (n:pos) (b:nat) =
neg_mul_left b n;
lemma_div_plus a (-b) n
val lemma_mod_plus_mul_distr: a:int -> b:int -> c:int -> p:pos -> Lemma
(((a + b) * c) % p = ((((a % p) + (b % p)) % p) * (c % p)) % p)
let lemma_mod_plus_mul_distr a b c p =
calc (==) {
((a + b) * c) % p;
== { lemma_mod_mul_distr_l (a + b) c p }
(((a + b) % p) * c) % p;
== { lemma_mod_mul_distr_r ((a + b) % p) c p }
(((a + b) % p) * (c % p)) % p;
== { modulo_distributivity a b p }
((((a % p) + (b % p)) % p) * (c % p)) % p;
}
(* Lemma: Modulo distributivity under special condition *)
val modulo_addition_lemma (a:int) (n:pos) (b:int) : Lemma ((a + b * n) % n = a % n)
let modulo_addition_lemma (a:int) (n:pos) (b:int) = lemma_mod_plus a b n
(* Lemma: Modulo distributivity under special condition *)
val lemma_mod_sub (a:int) (n:pos) (b:int) : Lemma (ensures (a - b * n) % n = a % n)
let lemma_mod_sub (a:int) (n:pos) (b:int) =
neg_mul_left b n;
lemma_mod_plus a (-b) n
val mod_mult_exact (a:int) (n:pos) (q:pos) : Lemma
(requires (a % (n * q) == 0))
(ensures a % n == 0)
let mod_mult_exact (a:int) (n:pos) (q:pos) =
calc (==) {
a % n;
== { lemma_div_mod a (n * q) }
((n * q) * (a / (n * q)) + a % (n * q)) % n;
== { (* hyp *) }
((n * q) * (a / (n * q))) % n;
== { paren_mul_right n q (a / (n * q));
swap_mul n (q * (a / (n * q))) }
((q * (a / (n * q))) * n) % n;
== { multiple_modulo_lemma (q * (a / (n*q))) n }
0;
}
val mod_mul_div_exact (a:int) (b:pos) (n:pos) : Lemma
(requires (a % (b * n) == 0))
(ensures (a / b) % n == 0)
let mod_mul_div_exact (a:int) (b:pos) (n:pos) =
calc (==) {
(a / b) % n;
== { lemma_div_mod a (b * n) (* + hyp *) }
(((b*n)*(a / (b*n))) / b) % n;
== { paren_mul_right b n (a / (b*n)) }
((b*(n*(a / (b*n)))) / b) % n;
== { cancel_mul_div (n * (a / (b * n))) b }
(n*(a / (b*n))) % n;
== { cancel_mul_mod (a / (b*n)) n }
0;
}
#push-options "--fuel 1"
val mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
let mod_pow2_div2 (a:int) (m:pos) : Lemma
(requires a % pow2 m == 0)
(ensures (a / 2) % pow2 (m - 1) == 0)
=
mod_mul_div_exact a 2 (pow2 (m - 1))
#pop-options
private val lemma_div_lt_cancel (a : int) (b : pos) (n : int) :
Lemma (requires (a < b * n))
(ensures (a / b < n))
private let lemma_div_lt_cancel a b n =
(* by contradiction *)
if a / b >= n then begin
calc (>=) {
a;
>= { slash_decr_axiom a b }
(a / b) * b;
>= {}
n * b;
};
assert False
end
private val lemma_mod_mult_zero (a : int) (b : pos) (c : pos) : Lemma ((a % (b * c)) / b / c == 0)
private let lemma_mod_mult_zero a b c =
(* < 1 *)
lemma_mod_lt a (b * c);
lemma_div_lt_cancel (a % (b * c)) b c;
lemma_div_lt_cancel ((a % (b * c)) / b) c 1;
(* >= 0 *)
nat_over_pos_is_nat (a % (b * c)) b;
nat_over_pos_is_nat ((a % (b * c)) / b) c;
()
(* Lemma: Divided by a product is equivalent to being divided one by one *)
val division_multiplication_lemma (a:int) (b:pos) (c:pos) : Lemma
(a / (b * c) = (a / b) / c)
let division_multiplication_lemma (a:int) (b:pos) (c:pos) =
calc (==) {
a / b / c;
== { lemma_div_mod a (b * c) }
((b * c) * (a / (b * c)) + a % (b * c)) / b / c;
== { paren_mul_right b c (a / (b * c)) }
(b * (c * (a / (b * c))) + a % (b * c)) / b / c;
== { lemma_div_plus (a % (b * c)) (c * (a / (b * c))) b }
(c * (a / (b * c)) + ((a % (b * c)) / b)) / c;
== { lemma_div_plus ((a % (b * c)) / b) (a / (b * c)) c }
(a / (b * c)) + (a % (b * c)) / b / c;
== { lemma_mod_mult_zero a b c }
a / (b * c);
}
private val cancel_fraction (a:int) (b:pos) (c:pos) : Lemma ((a * c) / (b * c) == a / b)
private let cancel_fraction a b c =
calc (==) {
(a * c) / (b * c);
== { swap_mul b c }
(a * c) / (c * b);
== { division_multiplication_lemma (a * c) c b }
((a * c) / c) / b;
== { cancel_mul_div a c }
a / b;
}
val modulo_scale_lemma : a:int -> b:pos -> c:pos -> Lemma ((a * b) % (b * c) == (a % c) * b)
let modulo_scale_lemma a b c =
calc (==) {
(a * b) % (b * c);
== { lemma_div_mod (a * b) (b * c) }
a * b - (b * c) * ((a * b) / (b * c));
== { cancel_fraction a c b }
a * b - (b * c) * (a / c);
== { paren_mul_right b c (a / c) }
a * b - b * (c * (a / c));
== { swap_mul b (c * (a / c)); distributivity_sub_left a (c * (a / c)) b }
(a - c * (a / c)) * b;
== { lemma_div_mod a c }
(a % c) * b;
}
let lemma_mul_pos_pos_is_pos (x:pos) (y:pos) : Lemma (x*y > 0) = ()
let lemma_mul_nat_pos_is_nat (x:nat) (y:pos) : Lemma (x*y >= 0) = ()
let modulo_division_lemma_0 (a:nat) (b:pos) (c:pos) : Lemma
(a / (b*c) <= a /\ (a - (a / (b * c)) * (b * c)) / b = a / b - ((a / (b * c)) * c))
= slash_decr_axiom a (b*c);
calc (==) {
(a / (b*c)) * (b * c);
== { swap_mul b c }
(a / (b*c)) * (c * b);
== { paren_mul_right (a / (b*c)) c b }
((a / (b*c)) * c) * b;
};
cut ((a / (b*c)) * (b * c) = ((a / (b * c)) * c) * b);
lemma_div_mod a (b*c);
division_sub_lemma a b ((a / (b*c)) * c);
()
val modulo_division_lemma: a:nat -> b:pos -> c:pos ->
Lemma ((a % (b * c)) / b = (a / b) % c)
let modulo_division_lemma a b c =
calc (==) {
(a % (b * c)) / b;
== { lemma_div_mod a (b * c) }
(a - (b * c) * (a / (b * c))) / b;
== { paren_mul_right b c ((a / (b * c))); neg_mul_right b (c * (a / (b * c))) }
(a + b * (-(c * (a / (b * c))))) / b;
== { lemma_div_plus a (-(c * (a / (b * c)))) b }
(a / b) - c * (a / (b * c));
== { division_multiplication_lemma a b c }
(a / b) - c * ((a / b) / c);
== { lemma_div_mod (a/b) c }
(a / b) % c;
}
val modulo_modulo_lemma (a:int) (b:pos) (c:pos) : Lemma
((a % (b * c)) % b = a % b) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.pos -> c: Prims.pos
-> FStar.Pervasives.Lemma (ensures a % (b * c) % b = a % b) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.eq2",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_Addition",
"Prims.op_Minus",
"Prims.op_Division",
"Prims.op_Subtraction",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Math.Lemmas.lemma_div_mod",
"Prims.squash",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Math.Lemmas.neg_mul_right",
"FStar.Math.Lemmas.lemma_mod_plus",
"FStar.Math.Lemmas.pos_times_pos_is_pos"
] | [] | false | false | true | false | false | let modulo_modulo_lemma (a: int) (b c: pos) =
| pos_times_pos_is_pos b c;
calc ( == ) {
(a % (b * c)) % b;
( == ) { calc ( == ) {
a % (b * c);
( == ) { lemma_div_mod a (b * c) }
a - (b * c) * (a / (b * c));
( == ) { paren_mul_right b c (a / (b * c)) }
a - b * (c * (a / (b * c)));
} }
(a - b * (c * (a / (b * c)))) % b;
( == ) { () }
(a + (- (b * (c * (a / (b * c)))))) % b;
( == ) { neg_mul_right b (c * (a / (b * c))) }
(a + (b * (- c * (a / (b * c))))) % b;
( == ) { () }
(a + (- c * (a / (b * c))) * b) % b;
( == ) { lemma_mod_plus a (- c * (a / (b * c))) b }
a % b;
} | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.precedes_wrap | val precedes_wrap (#a: Type) (x y: a) : GTot Type0 | val precedes_wrap (#a: Type) (x y: a) : GTot Type0 | let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 63,
"end_line": 35,
"start_col": 0,
"start_line": 35
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)] | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | x: a -> y: a -> Prims.GTot Type0 | Prims.GTot | [
"sometrivial"
] | [] | [
"Prims.precedes"
] | [] | false | false | false | false | true | let precedes_wrap (#a: Type) (x y: a) : GTot Type0 =
| precedes x y | false |
FStar.Math.Lemmas.fst | FStar.Math.Lemmas.lemma_div_le | val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d)) | val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b))
(ensures (a / d <= b / d)) | let lemma_div_le a b d =
calc (==>) {
(a <= b) <: Type0;
==> { lemma_div_mod a d; lemma_div_mod b d }
d * (a/d) + a%d <= d * (b/d) + b%d;
==> {}
d * (a/d) - d * (b/d) <= b%d - a%d;
==> {}
d * (a/d - b/d) <= b%d - a%d;
==> { (* a%d >= 0, and b%d < d*) }
d * (a/d - b/d) < d;
==> {}
a/d - b/d <= 0;
} | {
"file_name": "ulib/FStar.Math.Lemmas.fst",
"git_rev": "10183ea187da8e8c426b799df6c825e24c0767d3",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | {
"end_col": 3,
"end_line": 602,
"start_col": 0,
"start_line": 589
} | (*
Copyright 2008-2018 Microsoft Research
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Math.Lemmas
open FStar.Mul
open FStar.Math.Lib
#push-options "--fuel 0 --ifuel 0"
(* Lemma: definition of Euclidean division *)
val euclidean_div_axiom: a:int -> b:pos -> Lemma
(a - b * (a / b) >= 0 /\ a - b * (a / b) < b)
let euclidean_div_axiom a b = ()
val lemma_eucl_div_bound: a:int -> b:int -> q:int -> Lemma
(requires (a < q))
(ensures (a + q * b < q * (b+1)))
let lemma_eucl_div_bound a b q = ()
val lemma_mult_le_left: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (a * b <= a * c))
let lemma_mult_le_left a b c = ()
val lemma_mult_le_right: a:nat -> b:int -> c:int -> Lemma
(requires (b <= c))
(ensures (b * a <= c * a))
let lemma_mult_le_right a b c = ()
val lemma_mult_lt_left: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (a * b < a * c))
let lemma_mult_lt_left a b c = ()
val lemma_mult_lt_right: a:pos -> b:int -> c:int -> Lemma
(requires (b < c))
(ensures (b * a < c * a))
let lemma_mult_lt_right a b c = ()
let lemma_mult_lt_sqr (n:nat) (m:nat) (k:nat{n < k && m < k})
: Lemma (n * m < k * k) =
calc (<=) {
n * m;
<= { lemma_mult_le_left n m (k - 1) }
n * (k - 1);
<= { lemma_mult_le_right (k - 1) n (k - 1) }
(k - 1) * (k - 1);
<= {}
k*k - 1;
}
(* Lemma: multiplication on integers is commutative *)
val swap_mul: a:int -> b:int -> Lemma (a * b = b * a)
let swap_mul a b = ()
val lemma_cancel_mul (a b : int) (n : pos) : Lemma (requires (a * n = b * n)) (ensures (a = b))
let lemma_cancel_mul a b n = ()
(* Lemma: multiplication is right distributive over addition *)
val distributivity_add_left: a:int -> b:int -> c:int -> Lemma
((a + b) * c = a * c + b * c)
let distributivity_add_left a b c = ()
(* Lemma: multiplication is left distributive over addition *)
val distributivity_add_right: a:int -> b:int -> c:int -> Lemma
(a * (b + c) = a * b + a * c)
let distributivity_add_right a b c =
calc (==) {
a * (b + c);
== {}
(b + c) * a;
== { distributivity_add_left b c a }
b * a + c * a;
== {}
a * b + a * c;
}
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
(* GM: This is really just an identity since the LHS is associated to the left *)
val paren_mul_left: a:int -> b:int -> c:int -> Lemma
(a * b * c = (a * b) * c)
let paren_mul_left a b c = ()
(* Lemma: multiplication is associative, hence parenthesizing is meaningless *)
val paren_mul_right: a:int -> b:int -> c:int -> Lemma
(a * b * c = a * (b * c))
let paren_mul_right a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_left: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c)
let paren_add_left a b c = ()
(* Lemma: addition is associative, hence parenthesizing is meaningless *)
val paren_add_right: a:int -> b:int -> c:int -> Lemma
(a + b + c = a + (b + c))
let paren_add_right a b c = ()
val addition_is_associative: a:int -> b:int -> c:int -> Lemma
(a + b + c = (a + b) + c /\ a + b + c = a + (b + c))
let addition_is_associative a b c = ()
val subtraction_is_distributive: a:int -> b:int -> c:int -> Lemma
(a - b + c = (a - b) + c /\
a - b - c = a - (b + c) /\
a - b - c = (a - b) - c /\
a + (-b - c) = a - b - c /\
a - (b - c) = a - b + c)
let subtraction_is_distributive a b c = ()
val swap_add_plus_minus: a:int -> b:int -> c:int -> Lemma
(a + b - c = (a - c) + b)
let swap_add_plus_minus a b c = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_left: a:int -> b:int -> Lemma (-(a * b) = (-a) * b)
let neg_mul_left a b = ()
(* Lemma: minus applies to the whole term *)
val neg_mul_right: a:int -> b:int -> Lemma (-(a * b) = a * (-b))
let neg_mul_right a b = ()
val swap_neg_mul: a:int -> b:int -> Lemma ((-a) * b = a * (-b))
let swap_neg_mul a b =
neg_mul_left a b;
neg_mul_right a b
(* Lemma: multiplication is left distributive over subtraction *)
val distributivity_sub_left: a:int -> b:int -> c:int ->
Lemma ((a - b) * c = a * c - b * c)
let distributivity_sub_left a b c =
calc (==) {
(a - b) * c;
== {}
(a + (-b)) * c;
== { distributivity_add_left a (-b) c }
a * c + (-b) * c;
== { neg_mul_left b c }
a * c - b * c;
}
(* Lemma: multiplication is right distributive over subtraction *)
val distributivity_sub_right: a:int -> b:int -> c:int ->
Lemma ((a * (b - c) = a * b - a * c))
let distributivity_sub_right a b c =
calc (==) {
a * (b - c);
== {}
a * (b + (-c));
== { distributivity_add_right a b (-c) }
a * b + a * (-c);
== { neg_mul_right a c }
a * b - a * c;
}
(* Lemma: multiplication precedence on addition *)
val mul_binds_tighter: a:int -> b:int -> c:int -> Lemma (a + (b * c) = a + b * c)
let mul_binds_tighter a b c = ()
val lemma_abs_mul : a:int -> b:int -> Lemma (abs a * abs b = abs (a * b))
let lemma_abs_mul a b = ()
val lemma_abs_bound : a:int -> b:nat -> Lemma (abs a < b <==> -b < a /\ a < b)
let lemma_abs_bound a b = ()
(* Lemma: multiplication keeps symmetric bounds :
b > 0 && d > 0 && -b < a < b && -d < c < d ==> - b * d < a * c < b * d *)
val mul_ineq1: a:int -> b:nat -> c:int -> d:nat -> Lemma
(requires (-b < a /\ a < b /\
-d < c /\ c < d))
(ensures (-(b * d) < a * c /\ a * c < b * d))
let mul_ineq1 a b c d =
if a = 0 || c = 0 then ()
else begin
lemma_abs_bound a b;
lemma_abs_bound c d;
lemma_abs_mul a c;
lemma_mult_lt_left (abs a) (abs c) d;
lemma_mult_lt_right d (abs a) b;
lemma_abs_bound (a * c) (b * d);
()
end
(* Zero is neutral for addition *)
let add_zero_left_is_same (n : int) : Lemma(0 + n = n) = ()
let add_zero_right_is_same (n : int) : Lemma(n + 0 = n) = ()
(* One is neutral for multiplication *)
let mul_one_left_is_same (n : int) : Lemma(1 * n = n) = ()
let mul_one_right_is_same (n : int) : Lemma(n * 1 = n) = ()
(* Multiplying by zero gives zero *)
let mul_zero_left_is_zero (n : int) : Lemma(0 * n = 0) = ()
let mul_zero_right_is_zero (n : int) : Lemma(n * 0 = 0) = ()
val nat_times_nat_is_nat: a:nat -> b:nat -> Lemma (a * b >= 0)
let nat_times_nat_is_nat a b = ()
val pos_times_pos_is_pos: a:pos -> b:pos -> Lemma (a * b > 0)
let pos_times_pos_is_pos a b = ()
val nat_over_pos_is_nat: a:nat -> b:pos -> Lemma (a / b >= 0)
let nat_over_pos_is_nat a b = ()
val nat_plus_nat_equal_zero_lemma: a:nat -> b:nat{a + b = 0} -> Lemma(a = 0 /\ b = 0)
let nat_plus_nat_equal_zero_lemma a b = ()
val int_times_int_equal_zero_lemma: a:int -> b:int{a * b = 0} -> Lemma(a = 0 \/ b = 0)
let int_times_int_equal_zero_lemma a b = ()
#push-options "--fuel 1"
val pow2_double_sum: n:nat -> Lemma (pow2 n + pow2 n = pow2 (n + 1))
let pow2_double_sum n = ()
val pow2_double_mult: n:nat -> Lemma (2 * pow2 n = pow2 (n + 1))
let pow2_double_mult n = pow2_double_sum n
val pow2_lt_compat: n:nat -> m:nat -> Lemma
(requires (m < n))
(ensures (pow2 m < pow2 n))
(decreases m)
let rec pow2_lt_compat n m =
match m with
| 0 -> ()
| _ -> pow2_lt_compat (n-1) (m-1)
#pop-options
val pow2_le_compat: n:nat -> m:nat -> Lemma
(requires (m <= n))
(ensures (pow2 m <= pow2 n))
let pow2_le_compat n m =
if m < n then pow2_lt_compat n m
#push-options "--fuel 1"
val pow2_plus: n:nat -> m:nat -> Lemma
(ensures (pow2 n * pow2 m = pow2 (n + m)))
(decreases n)
let rec pow2_plus n m =
match n with
| 0 -> ()
| _ -> pow2_plus (n - 1) m
#pop-options
(* Lemma : definition of the exponential property of pow2 *)
val pow2_minus: n:nat -> m:nat{ n >= m } -> Lemma
((pow2 n) / (pow2 m) = pow2 (n - m))
let pow2_minus n m =
pow2_plus (n - m) m;
slash_star_axiom (pow2 (n - m)) (pow2 m) (pow2 n)
(* Lemma: loss of precision in euclidean division *)
val multiply_fractions (a:int) (n:nonzero) : Lemma (n * ( a / n ) <= a)
let multiply_fractions a n = ()
(** Same as `small_mod` *)
val modulo_lemma: a:nat -> b:pos -> Lemma (requires (a < b)) (ensures (a % b = a))
let modulo_lemma a b = ()
(** Same as `lemma_div_def` in Math.Lib *)
val lemma_div_mod: a:int -> p:nonzero -> Lemma (a = p * (a / p) + a % p)
let lemma_div_mod a p = ()
val lemma_mod_lt: a:int -> p:pos -> Lemma (0 <= a % p /\ a % p < p /\ (a >= 0 ==> a % p <= a))
let lemma_mod_lt a p = ()
val lemma_div_lt_nat: a:int -> n:nat -> m:nat{m <= n} ->
Lemma (requires (a < pow2 n))
(ensures (a / pow2 m < pow2 (n-m)))
let lemma_div_lt_nat a n m =
lemma_div_mod a (pow2 m);
assert(a = pow2 m * (a / pow2 m) + a % pow2 m);
pow2_plus m (n-m);
assert(pow2 n = pow2 m * pow2 (n - m))
val lemma_div_lt (a:int) (n:nat) (m:nat) : Lemma
(requires m <= n /\ a < pow2 n)
(ensures a / pow2 m < pow2 (n-m))
let lemma_div_lt a n m =
if a >= 0 then lemma_div_lt_nat a n m
val bounded_multiple_is_zero (x:int) (n:pos) : Lemma
(requires -n < x * n /\ x * n < n)
(ensures x == 0)
let bounded_multiple_is_zero (x:int) (n:pos) = ()
val small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0)
let small_div (a:nat) (n:pos) : Lemma (requires a < n) (ensures a / n == 0) = ()
val small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a)
let small_mod (a:nat) (n:pos) : Lemma (requires a < n) (ensures a % n == a) = ()
val lt_multiple_is_equal (a:nat) (b:nat) (x:int) (n:nonzero) : Lemma
(requires a < n /\ b < n /\ a == b + x * n)
(ensures a == b /\ x == 0)
let lt_multiple_is_equal a b x n =
assert (0 * n == 0);
bounded_multiple_is_zero x n
val lemma_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) % n = a % n)
let lemma_mod_plus (a:int) (k:int) (n:pos) =
calc (==) {
(a+k*n)%n - a%n;
== { lemma_div_mod a n; lemma_div_mod (a+k*n) n }
((a + k*n) - n*((a + k*n)/n)) - (a - n*(a/n));
== {}
n*k + n*(a/n) - n*((a + k*n)/n);
== { distributivity_add_right n k (a/n);
distributivity_sub_right n (k + a/n) ((a + k*n)/n) }
n * (k + a/n - (a+k*n)/n);
};
lt_multiple_is_equal ((a+k*n)%n) (a%n) (k + a/n - (a+k*n)/n) n;
()
val lemma_div_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k)
let lemma_div_plus (a:int) (k:int) (n:pos) =
calc (==) {
n * ((a+k*n)/n - a/n);
== { distributivity_sub_right n ((a+k*n)/n) (a/n) }
n * ((a+k*n)/n) - n*(a/n);
== { lemma_div_mod (a+k*n) n; lemma_div_mod a n }
(a + k*n - (a+k*n)%n) - (a - a%n);
== {}
k*n - (a+k*n)%n + a%n;
== { lemma_mod_plus a k n }
k*n;
};
lemma_cancel_mul ((a+k*n)/n - a/n) k n
let lemma_div_mod_plus (a:int) (k:int) (n:pos) : Lemma ((a + k * n) / n = a / n + k /\
(a + k * n) % n = a % n) =
lemma_div_plus a k n;
lemma_mod_plus a k n
val add_div_mod_1 (a:int) (n:pos) : Lemma ((a + n) % n == a % n /\ (a + n) / n == a / n + 1)
let add_div_mod_1 a n =
lemma_mod_plus a 1 n;
lemma_div_plus a 1 n
val sub_div_mod_1 (a:int) (n:pos) : Lemma ((a - n) % n == a % n /\ (a - n) / n == a / n - 1)
let sub_div_mod_1 a n =
lemma_mod_plus a (-1) n;
lemma_div_plus a (-1) n
#push-options "--smtencoding.elim_box true --smtencoding.nl_arith_repr native"
val cancel_mul_div (a:int) (n:nonzero) : Lemma ((a * n) / n == a)
let cancel_mul_div (a:int) (n:nonzero) = ()
#pop-options
val cancel_mul_mod (a:int) (n:pos) : Lemma ((a * n) % n == 0)
let cancel_mul_mod (a:int) (n:pos) =
small_mod 0 n;
lemma_mod_plus 0 a n
val lemma_mod_add_distr (a:int) (b:int) (n:pos) : Lemma ((a + b % n) % n = (a + b) % n)
let lemma_mod_add_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a + b%n) % n;
== { lemma_mod_plus (a + (b % n)) (b / n) n }
(a + b%n + n * (b/n)) % n;
== { lemma_div_mod b n }
(a + b) % n;
}
val lemma_mod_sub_distr (a:int) (b:int) (n:pos) : Lemma ((a - b % n) % n = (a - b) % n)
let lemma_mod_sub_distr (a:int) (b:int) (n:pos) =
calc (==) {
(a - b%n) % n;
== { lemma_mod_plus (a - (b % n)) (-(b / n)) n }
(a - b%n + n * (-(b/n))) % n;
== { neg_mul_right n (b/n) }
(a - b%n - n * (b/n)) % n;
== { lemma_div_mod b n }
(a - b) % n;
}
val lemma_mod_sub_0: a:pos -> Lemma ((-1) % a = a - 1)
let lemma_mod_sub_0 a = ()
val lemma_mod_sub_1: a:pos -> b:pos{a < b} -> Lemma ((-a) % b = b - (a%b))
let lemma_mod_sub_1 a b =
calc (==) {
(-a) % b;
== { lemma_mod_plus (-a) 1 b }
((-a) + 1*b) % b;
== {}
(b - a) % b;
== { small_mod (b-a) b }
b - a;
== { small_mod a b }
b - a%b;
}
val lemma_mod_mul_distr_l (a:int) (b:int) (n:pos) : Lemma
(requires True)
(ensures (a * b) % n = ((a % n) * b) % n)
let lemma_mod_mul_distr_l a b n =
calc (==) {
(a * b) % n;
== { lemma_div_mod a n }
((n * (a/n) + a%n) * b) % n;
== { distributivity_add_left (n * (a/n)) (a%n) b }
(n * (a/n) * b + (a%n) * b) % n;
== { paren_mul_right n (a/n) b; swap_mul ((a/n) * b) n }
((a%n) * b + ((a/n) * b) * n) % n;
== { lemma_mod_plus ((a%n) * b) ((a/n) * b) n }
((a%n) * b) % n;
}
val lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) : Lemma ((a * b) % n = (a * (b % n)) % n)
let lemma_mod_mul_distr_r (a:int) (b:int) (n:pos) =
calc (==) {
(a * b) % n;
== { swap_mul a b }
(b * a) % n;
== { lemma_mod_mul_distr_l b a n }
(b%n * a) % n;
== { swap_mul a (b%n) }
(a * (b%n)) % n;
}
val lemma_mod_injective: p:pos -> a:nat -> b:nat -> Lemma
(requires (a < p /\ b < p /\ a % p = b % p))
(ensures (a = b))
let lemma_mod_injective p a b = ()
val lemma_mul_sub_distr: a:int -> b:int -> c:int -> Lemma
(a * b - a * c = a * (b - c))
let lemma_mul_sub_distr a b c =
distributivity_sub_right a b c
val lemma_div_exact: a:int -> p:pos -> Lemma
(requires (a % p = 0))
(ensures (a = p * (a / p)))
let lemma_div_exact a p = ()
val div_exact_r (a:int) (n:pos) : Lemma
(requires (a % n = 0))
(ensures (a = (a / n) * n))
let div_exact_r (a:int) (n:pos) = lemma_div_exact a n
val lemma_mod_spec: a:int -> p:pos -> Lemma
(a / p = (a - (a % p)) / p)
let lemma_mod_spec a p =
calc (==) {
(a - a%p)/p;
== { lemma_div_mod a p }
(p*(a/p))/p;
== { cancel_mul_div (a/p) p }
a/p;
}
val lemma_mod_spec2: a:int -> p:pos -> Lemma
(let q:int = (a - (a % p)) / p in a = (a % p) + q * p)
let lemma_mod_spec2 a p =
calc (==) {
(a % p) + ((a - (a % p)) / p) * p;
== { lemma_mod_spec a p }
(a % p) + (a / p) * p;
== { lemma_div_mod a p }
a;
}
val lemma_mod_plus_distr_l: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = ((a % p) + b) % p)
let lemma_mod_plus_distr_l a b p =
let q = (a - (a % p)) / p in
lemma_mod_spec2 a p;
lemma_mod_plus (a % p + b) q p
val lemma_mod_plus_distr_r: a:int -> b:int -> p:pos -> Lemma
((a + b) % p = (a + (b % p)) % p)
let lemma_mod_plus_distr_r a b p =
lemma_mod_plus_distr_l b a p
val lemma_mod_mod: a:int -> b:int -> p:pos -> Lemma
(requires (a = b % p))
(ensures (a % p = b % p))
let lemma_mod_mod a b p =
lemma_mod_lt b p;
modulo_lemma (b % p) p
(* * Lemmas about multiplication, division and modulo. **)
(* * This part focuses on the situation where **)
(* * dividend: nat divisor: pos **)
(* * TODO: add triggers for certain lemmas. **)
(* Lemma: Definition of euclidean division *)
val euclidean_division_definition: a:int -> b:nonzero ->
Lemma (a = (a / b) * b + a % b)
let euclidean_division_definition a b = ()
(* Lemma: Propriety about modulo *)
val modulo_range_lemma: a:int -> b:pos ->
Lemma (a % b >= 0 && a % b < b)
let modulo_range_lemma a b = ()
val small_modulo_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a % b = a)
let small_modulo_lemma_1 a b = ()
val small_modulo_lemma_2: a:int -> b:pos ->
Lemma (requires a % b = a) (ensures a < b)
let small_modulo_lemma_2 a b = ()
val small_division_lemma_1: a:nat -> b:nonzero ->
Lemma (requires a < b) (ensures a / b = 0)
let small_division_lemma_1 a b = ()
val small_division_lemma_2 (a:int) (n:pos) : Lemma
(requires a / n = 0)
(ensures 0 <= a /\ a < n)
let small_division_lemma_2 (a:int) (n:pos) = lemma_div_mod a n
(* Lemma: Multiplication by a positive integer preserves order *)
val multiplication_order_lemma: a:int -> b:int -> p:pos ->
Lemma (a >= b <==> a * p >= b * p)
let multiplication_order_lemma a b p = ()
(* Lemma: Propriety about multiplication after division *)
val division_propriety: a:int -> b:pos ->
Lemma (a - b < (a / b) * b && (a / b) * b <= a)
let division_propriety a b = ()
(* Internal lemmas for proving the definition of division *)
val division_definition_lemma_1: a:int -> b:pos -> m:int{a - b < m * b} ->
Lemma (m > a / b - 1)
let division_definition_lemma_1 a b m =
if a / b - 1 < 0 then () else begin
division_propriety a b;
multiplication_order_lemma m (a / b - 1) b
end
val division_definition_lemma_2: a:int -> b:pos -> m:int{m * b <= a} ->
Lemma (m < a / b + 1)
let division_definition_lemma_2 a b m =
division_propriety a b;
multiplication_order_lemma (a / b + 1) m b
(* Lemma: Definition of division *)
val division_definition: a:int -> b:pos -> m:int{a - b < m * b && m * b <= a} ->
Lemma (m = a / b)
let division_definition a b m =
division_definition_lemma_1 a b m;
division_definition_lemma_2 a b m
(* Lemma: (a * b) / b = a; identical to `cancel_mul_div` above *)
val multiple_division_lemma (a:int) (n:nonzero) : Lemma ((a * n) / n = a)
let multiple_division_lemma (a:int) (n:nonzero) = cancel_mul_div a n
(* Lemma: (a * b) % b = 0 *)
val multiple_modulo_lemma (a:int) (n:pos) : Lemma ((a * n) % n = 0)
let multiple_modulo_lemma (a:int) (n:pos) = cancel_mul_mod a n
(* Lemma: Division distributivity under special condition *)
val division_addition_lemma: a:int -> b:pos -> n:int ->
Lemma ( (a + n * b) / b = a / b + n )
let division_addition_lemma a b n = division_definition (a + n * b) b (a / b + n)
(* Lemma: Modulo distributivity *)
val modulo_distributivity: a:int -> b:int -> c:pos -> Lemma ((a + b) % c == (a % c + b % c) % c)
let modulo_distributivity a b c =
calc (==) {
(a + b) % c;
== { lemma_mod_plus_distr_l a b c }
((a % c) + b) % c;
== { lemma_mod_plus_distr_r (a % c) b c }
((a % c) + (b % c)) % c;
}
val lemma_div_le: a:int -> b:int -> d:pos ->
Lemma (requires (a <= b)) | {
"checked_file": "/",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lib.fst.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Math.Lemmas.fst"
} | [
{
"abbrev": false,
"full_module": "FStar.Math.Lib",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | a: Prims.int -> b: Prims.int -> d: Prims.pos
-> FStar.Pervasives.Lemma (requires a <= b) (ensures a / d <= b / d) | FStar.Pervasives.Lemma | [
"lemma"
] | [] | [
"Prims.int",
"Prims.pos",
"FStar.Calc.calc_finish",
"Prims.logical",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Subtraction",
"Prims.op_Division",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"Prims.unit",
"FStar.Calc.calc_step",
"Prims.op_LessThan",
"FStar.Mul.op_Star",
"Prims.op_Modulus",
"Prims.op_Addition",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Calc.calc_push_impl",
"Prims.squash",
"FStar.Math.Lemmas.lemma_div_mod"
] | [] | false | false | true | false | false | let lemma_div_le a b d =
| calc ( ==> ) {
(a <= b) <: Type0;
( ==> ) { (lemma_div_mod a d;
lemma_div_mod b d) }
d * (a / d) + a % d <= d * (b / d) + b % d;
( ==> ) { () }
d * (a / d) - d * (b / d) <= b % d - a % d;
( ==> ) { () }
d * (a / d - b / d) <= b % d - a % d;
( ==> ) { () }
d * (a / d - b / d) < d;
( ==> ) { () }
a / d - b / d <= 0;
} | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_lemma_Poly1305_blocks_while0 | val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0)))))))))))))) | val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0)))))))))))))) | let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 31,
"end_line": 1227,
"start_col": 0,
"start_line": 1144
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0)))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
va_b0: Vale.X64.Decls.va_code ->
va_s0: Vale.X64.Decls.va_state ->
va_old: Vale.X64.Decls.va_state ->
va_in_ctx_b: Vale.X64.Memory.buffer64 ->
va_in_h_in: Prims.int ->
va_in_inp_b: Vale.X64.Memory.buffer64 ->
va_in_length: Prims.int ->
va_in_n: Vale.X64.Decls.va_int_range 18446744073709551616 18446744073709551616 ->
va_in_p:
Vale.X64.Decls.va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819 ->
va_in_r: Prims.int ->
va_in_h: Prims.int ->
va_in_word_index: Prims.nat
-> Prims.Ghost (((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.int) * Prims.nat) | Prims.Ghost | [] | [] | [
"Vale.X64.Decls.va_code",
"Vale.X64.Decls.va_state",
"Vale.X64.Memory.buffer64",
"Prims.int",
"Vale.X64.Decls.va_int_range",
"Prims.nat",
"Vale.X64.QuickCodes.fuel",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.Mktuple4",
"Vale.X64.Decls.va_fuel",
"FStar.Pervasives.Native.tuple4",
"Prims.unit",
"Vale.X64.QuickCode.va_lemma_norm_mods",
"Prims.Cons",
"Vale.X64.QuickCode.mod_t",
"Vale.X64.QuickCode.va_Mod_reg64",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Machine_s.rR9",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rR15",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR10",
"Vale.X64.QuickCode.va_Mod_ok",
"Vale.X64.QuickCode.va_Mod_flags",
"Prims.Nil",
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.list",
"Vale.X64.QuickCode.__proj__QProc__item__mods",
"Vale.Poly1305.X64.va_code_Poly1305_blocks_while0",
"FStar.Pervasives.Native.tuple3",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCodes.va_wp_sound_code_norm",
"Prims.l_and",
"Vale.X64.QuickCodes.label",
"Vale.X64.QuickCodes.va_range1",
"Prims.b2t",
"Vale.X64.Decls.va_get_ok",
"Vale.X64.Machine_s.pow2_64",
"Vale.X64.Decls.va_mul_nat",
"Prims.op_Subtraction",
"Prims.op_Multiply",
"Prims.op_Addition",
"Vale.X64.Decls.va_get_reg64",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR11",
"Prims.op_LessThan",
"Prims.op_Division",
"Prims.op_Modulus",
"Vale.X64.Machine_s.rR13",
"Vale.Def.Types_s.nat64",
"Prims.l_imp",
"Prims.l_not",
"Prims.op_LessThanOrEqual",
"Vale.X64.Memory.buffer_addr",
"Vale.X64.Memory.vuint64",
"Vale.X64.Decls.va_get_mem_heaplet",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Decls.validDstAddrs64",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Decls.va_get_mem_layout",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.Decls.validSrcAddrs64",
"Vale.Poly1305.Spec_s.modp",
"Vale.Poly1305.Util.poly1305_heap_blocks",
"Vale.X64.Decls.buffer64_as_seq",
"Vale.X64.Decls.vale_heap",
"Vale.X64.QuickCode.quickCode",
"Vale.Poly1305.X64.va_qcode_Poly1305_blocks_while0",
"Vale.X64.Decls.va_expand_state"
] | [] | false | false | false | false | false | let va_lemma_Poly1305_blocks_while0
va_b0
va_s0
va_old
va_in_ctx_b
va_in_h_in
va_in_inp_b
va_in_length
va_in_n
va_in_p
va_in_r
va_in_h
va_in_word_index
=
| let va_old = va_expand_state va_old in
let va_mods:va_mods_t =
[
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_ok; va_Mod_flags
]
in
let va_qc =
va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index
in
let va_sM, va_fM, va_g =
va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ())
va_qc
va_s0
(fun va_s0 va_sM va_g ->
let h, word_index = va_g in
label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == (va_mul_nat va_in_n va_in_n) `op_Multiply` 4 - 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) +
va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rR12 va_sM) `op_Modulus` 4 == 0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + (va_get_reg64 rR12 va_sM) `op_Division` 4) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` (va_get_reg64 rR15 va_sM) ==
va_get_reg64 rRsi va_old + va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` (va_get_reg64 rR15 va_sM) + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b
(va_get_mem_heaplet 0 va_sM) +
8
`op_Multiply`
word_index) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rR15 va_sM) `op_Multiply` 16 <= va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM)
va_in_ctx_b
24
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_old)
va_in_inp_b
(va_in_length `op_Division` 8)
(va_get_mem_layout va_sM)
Public) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in)
(va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n))
va_in_r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) va_in_inp_b)
word_index) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0)))
in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([
va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_ok; va_Mod_flags
])
va_sM
va_s0;
let h, word_index = va_g in
(va_sM, va_fM, h, word_index) | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.va_QEmpty | val va_QEmpty (#a: Type0) (v: a) : quickCodes a [] | val va_QEmpty (#a: Type0) (v: a) : quickCodes a [] | let va_QEmpty (#a:Type0) (v:a) : quickCodes a [] = QEmpty v | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 78,
"end_line": 73,
"start_col": 19,
"start_line": 73
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)]
// wrap "precedes" and LexCons to avoid issues with label (precedes ...)
let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y
[@va_qattr]
let rec mods_contains1 (allowed:mods_t) (found:mod_t) : bool =
match allowed with
| [] -> mod_eq Mod_None found
| h::t -> mod_eq h found || mods_contains1 t found
[@va_qattr]
let rec mods_contains (allowed:mods_t) (found:mods_t) : bool =
match found with
| [] -> true
| h::t -> mods_contains1 allowed h && mods_contains allowed t
[@va_qattr]
let if_code (b:bool) (c1:code) (c2:code) : code = if b then c1 else c2
open FStar.Monotonic.Pure
noeq type quickCodes (a:Type0) : codes -> Type =
| QEmpty: a -> quickCodes a []
| QSeq: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> quickCodes a cs -> quickCodes a (c::cs)
| QBind: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a (c::cs)
| QGetState: #cs:codes -> (va_state -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QPURE: #cs:codes -> r:range -> msg:string -> pre:((unit -> GTot Type0) -> GTot Type0){is_monotonic pre} ->
(unit -> PURE unit (as_pure_wp pre)) -> quickCodes a cs -> quickCodes a cs
//| QBindPURE: #cs:codes -> b:Type -> r:range -> msg:string -> pre:((b -> GTot Type0) -> GTot Type0) ->
// (unit -> PURE b pre) -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QLemma: #cs:codes -> r:range -> msg:string -> pre:Type0 -> post:(squash pre -> Type0) ->
(unit -> Lemma (requires pre) (ensures post ())) -> quickCodes a cs -> quickCodes a cs
| QGhost: #cs:codes -> b:Type -> r:range -> msg:string -> pre:Type0 -> post:(b -> Type0) ->
(unit -> Ghost b (requires pre) (ensures post)) -> (b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QAssertBy: #cs:codes -> r:range -> msg:string -> p:Type0 ->
quickCodes unit [] -> quickCodes a cs -> quickCodes a cs | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "FStar.Monotonic.Pure",
"short_module": null
},
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | v: a -> Vale.X64.QuickCodes.quickCodes a [] | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCodes.QEmpty",
"Vale.X64.QuickCodes.quickCodes",
"Prims.Nil",
"Vale.X64.Machine_s.precode",
"Vale.X64.Decls.ins",
"Vale.X64.Decls.ocmp"
] | [] | false | false | false | true | false | let va_QEmpty (#a: Type0) (v: a) : quickCodes a [] =
| QEmpty v | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.if_code | val if_code (b: bool) (c1 c2: code) : code | val if_code (b: bool) (c1 c2: code) : code | let if_code (b:bool) (c1:code) (c2:code) : code = if b then c1 else c2 | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 70,
"end_line": 50,
"start_col": 0,
"start_line": 50
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)]
// wrap "precedes" and LexCons to avoid issues with label (precedes ...)
let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y
[@va_qattr]
let rec mods_contains1 (allowed:mods_t) (found:mod_t) : bool =
match allowed with
| [] -> mod_eq Mod_None found
| h::t -> mod_eq h found || mods_contains1 t found
[@va_qattr]
let rec mods_contains (allowed:mods_t) (found:mods_t) : bool =
match found with
| [] -> true
| h::t -> mods_contains1 allowed h && mods_contains allowed t | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false | b: Prims.bool -> c1: Vale.X64.QuickCodes.code -> c2: Vale.X64.QuickCodes.code
-> Vale.X64.QuickCodes.code | Prims.Tot | [
"total"
] | [] | [
"Prims.bool",
"Vale.X64.QuickCodes.code"
] | [] | false | false | false | true | false | let if_code (b: bool) (c1 c2: code) : code =
| if b then c1 else c2 | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.va_QSeq | val va_QSeq
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: quickCodes a cs)
: quickCodes a (c :: cs) | val va_QSeq
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: quickCodes a cs)
: quickCodes a (c :: cs) | let va_QSeq (#a:Type0) (#b:Type) (#c:code) (#cs:codes) (r:range) (msg:string) (qc:quickCode b c) (qcs:quickCodes a cs) : quickCodes a (c::cs) = QSeq r msg qc qcs | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 180,
"end_line": 75,
"start_col": 19,
"start_line": 75
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)]
// wrap "precedes" and LexCons to avoid issues with label (precedes ...)
let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y
[@va_qattr]
let rec mods_contains1 (allowed:mods_t) (found:mod_t) : bool =
match allowed with
| [] -> mod_eq Mod_None found
| h::t -> mod_eq h found || mods_contains1 t found
[@va_qattr]
let rec mods_contains (allowed:mods_t) (found:mods_t) : bool =
match found with
| [] -> true
| h::t -> mods_contains1 allowed h && mods_contains allowed t
[@va_qattr]
let if_code (b:bool) (c1:code) (c2:code) : code = if b then c1 else c2
open FStar.Monotonic.Pure
noeq type quickCodes (a:Type0) : codes -> Type =
| QEmpty: a -> quickCodes a []
| QSeq: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> quickCodes a cs -> quickCodes a (c::cs)
| QBind: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a (c::cs)
| QGetState: #cs:codes -> (va_state -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QPURE: #cs:codes -> r:range -> msg:string -> pre:((unit -> GTot Type0) -> GTot Type0){is_monotonic pre} ->
(unit -> PURE unit (as_pure_wp pre)) -> quickCodes a cs -> quickCodes a cs
//| QBindPURE: #cs:codes -> b:Type -> r:range -> msg:string -> pre:((b -> GTot Type0) -> GTot Type0) ->
// (unit -> PURE b pre) -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QLemma: #cs:codes -> r:range -> msg:string -> pre:Type0 -> post:(squash pre -> Type0) ->
(unit -> Lemma (requires pre) (ensures post ())) -> quickCodes a cs -> quickCodes a cs
| QGhost: #cs:codes -> b:Type -> r:range -> msg:string -> pre:Type0 -> post:(b -> Type0) ->
(unit -> Ghost b (requires pre) (ensures post)) -> (b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QAssertBy: #cs:codes -> r:range -> msg:string -> p:Type0 ->
quickCodes unit [] -> quickCodes a cs -> quickCodes a cs
[@va_qattr] unfold let va_QBind (#a:Type0) (#b:Type) (#c:code) (#cs:codes) (r:range) (msg:string) (qc:quickCode b c) (qcs:va_state -> b -> GTot (quickCodes a cs)) : quickCodes a (c::cs) = QBind r msg qc qcs
[@va_qattr] unfold let va_QEmpty (#a:Type0) (v:a) : quickCodes a [] = QEmpty v | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "FStar.Monotonic.Pure",
"short_module": null
},
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
r: FStar.Range.range ->
msg: Prims.string ->
qc: Vale.X64.QuickCode.quickCode b c ->
qcs: Vale.X64.QuickCodes.quickCodes a cs
-> Vale.X64.QuickCodes.quickCodes a (c :: cs) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCodes.code",
"Vale.X64.QuickCodes.codes",
"FStar.Range.range",
"Prims.string",
"Vale.X64.QuickCode.quickCode",
"Vale.X64.QuickCodes.quickCodes",
"Vale.X64.QuickCodes.QSeq",
"Prims.Cons",
"Vale.X64.Decls.va_code"
] | [] | false | false | false | false | false | let va_QSeq
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: quickCodes a cs)
: quickCodes a (c :: cs) =
| QSeq r msg qc qcs | false |
Vale.Poly1305.X64.fst | Vale.Poly1305.X64.va_qcode_Poly1305 | val va_qcode_Poly1305
(va_mods: va_mods_t)
(win: bool)
(ctx_b inp_b: buffer64)
(len_in finish_in: nat64)
: (va_quickCode unit (va_code_Poly1305 win)) | val va_qcode_Poly1305
(va_mods: va_mods_t)
(win: bool)
(ctx_b inp_b: buffer64)
(len_in finish_in: nat64)
: (va_quickCode unit (va_code_Poly1305 win)) | let va_qcode_Poly1305 (va_mods:va_mods_t) (win:bool) (ctx_b:buffer64) (inp_b:buffer64)
(len_in:nat64) (finish_in:nat64) : (va_quickCode unit (va_code_Poly1305 win)) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(ctx_in:(va_int_range 0 18446744073709551615)) = va_if win (fun _ -> va_get_reg64 rRcx va_s)
(fun _ -> va_get_reg64 rRdi va_s) in let (inp_in:(va_int_range 0 18446744073709551615)) = va_if
win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s) in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 754 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_CreateHeaplets ([declare_buffer64 inp_b 0 Public Immutable; declare_buffer64 ctx_b 1
Public Mutable])) (fun (va_s:va_state) _ -> let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in let (key_s0:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 5
(va_get_mem_heaplet 1 va_s) in let (key_s1:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s) in let
(key_r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 in let
(key_s:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 key_s0 key_s1 in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 764 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 765 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi)) (fun (va_s:va_state) _
-> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 766 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qInlineIf va_mods win (qblock va_mods (fun (va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 768 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 769 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 770 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 771 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_QEmpty (())))))))
(qblock va_mods (fun (va_s:va_state) -> va_QEmpty (())))) (fun (va_s:va_state) va_g -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 785 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRcx) 184 Public ctx_b 23) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 788 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 789 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 790 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 791 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 792 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 793 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 794 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 795 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 797 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_impl key_r key_s ctx_b inp_b finish_in) (fun (va_s:va_state) (h':int) ->
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 799 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 800 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 801 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 804 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 805 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 806 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 807 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rR12)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 808 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 809 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 810 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 811 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 813 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 815 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_DestroyHeaplets ()) (va_QEmpty (())))))))))))))))))))))))))))))) | {
"file_name": "obj/Vale.Poly1305.X64.fst",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 78,
"end_line": 2900,
"start_col": 0,
"start_line": 2813
} | module Vale.Poly1305.X64
open Vale.Def.Opaque_s
open Vale.Def.Types_s
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.InsBasic
open Vale.X64.InsMem
open Vale.X64.InsStack
open Vale.X64.QuickCode
open Vale.X64.QuickCodes
open Vale.Poly1305.Spec_s
open Vale.Poly1305.Math
open Vale.Poly1305.Util
#reset-options "--z3rlimit 40"
//-- Poly1305_multiply
val va_code_Poly1305_multiply : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_multiply () =
(va_Block (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap
(va_op_opr64_reg64 rR14)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR11)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_CCons
(va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRbp)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRdx)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR13)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10)
(va_const_opr64 0)) (va_CCons (va_code_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64
rR11)) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CNil
()))))))))))))))))))))))))))
val va_codegen_success_Poly1305_multiply : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_multiply () =
(va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRdx)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR13)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR9)
(va_op_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rR10) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_IMul64 (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rR11)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRax) (va_const_opr64 18446744073709551612)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_ttrue ())))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_multiply (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_multiply ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 93 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR14 va_s) r1 == va_mul_nat r1 (va_get_reg64 rR14 va_s)) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 94 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rR14 va_s) == va_mul_nat (va_get_reg64 rR14
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 95 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR11 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR11 va_s)) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 97 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat (va_get_reg64 rR13 va_s) (va_get_reg64 rRbx va_s) == va_mul_nat (va_get_reg64 rRbx
va_s) (va_get_reg64 rR13 va_s)) (let (gd0:int) = va_mul_nat (va_get_reg64 rR14 va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbx va_s) (va_get_reg64 rR13 va_s) in let
(gd1:int) = va_mul_nat (va_get_reg64 rR14 va_s) r1 + va_mul_nat (va_get_reg64 rRbx va_s)
(va_get_reg64 rR11 va_s) + va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR13 va_s) in let
(gd2:int) = va_mul_nat (va_get_reg64 rRbp va_s) (va_get_reg64 rR11 va_s) in va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 105 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.va_is_src_opr64 (Vale.X64.Decls.va_op_opr64_reg64 rR14) va_s) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 106 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 107 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 108 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 109 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 112 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 113 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 114 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 115 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 118 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 119 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 120 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 121 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 124 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mul64Wrap (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 125 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 126 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 127 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 130 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 131 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 132 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 133 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 136 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_IMul64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR11)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 138 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 139 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 18446744073709551612)) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 140 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (fun (va_s:va_state)
_ -> let (hh:int) = va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_s) + va_mul_nat n
(va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in let (va_arg61:Prims.int) = hh in let
(va_arg60:Prims.int) = gd2 in let (va_arg59:Prims.int) = gd1 in let (va_arg58:Prims.int) = gd0
in let (va_arg57:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg56:Prims.int) = va_get_reg64
rRbp va_old_s in let (va_arg55:Prims.int) = va_get_reg64 rRbx va_old_s in let
(va_arg54:Prims.int) = va_get_reg64 rR14 va_old_s in let (va_arg53:Prims.int) = r1 in let
(va_arg52:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg51:Prims.int) = h in let
(va_arg50:Prims.int) = r in let (va_arg49:Prims.int) = p in let (va_arg48:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 144 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_multiply va_arg48 va_arg49 va_arg50 va_arg51
va_arg52 va_arg53 va_arg54 va_arg55 va_arg56 va_arg57 va_arg58 va_arg59 va_arg60 va_arg61)
(va_QEmpty ((hh))))))))))))))))))))))))))))))))))
val va_lemma_Poly1305_multiply : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_multiply ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1
`op_Division` 4 /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7
`op_Multiply` (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) <
va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64
rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0)
(va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp
va_s0) (va_get_reg64 rR13 va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) /\ va_state_eq
va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_multiply va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_multiply va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_multiply ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 62 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 88 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 89 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 90 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM
`op_Division` 4 < 18446744073709551616) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 91 column 37 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == 18446744073709551612))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_multiply (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_mul_nat
(va_get_reg64 rRbp va_s0) (va_get_reg64 rR11 va_s0) < 7 `op_Multiply` (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rR14 va_s0) r1 < va_mul_nat n (n `op_Division` 16) /\ va_mul_nat
(va_get_reg64 rRbx va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n `op_Division` 16) /\
va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13 va_s0) < va_mul_nat n (n `op_Division`
8) /\ va_mul_nat (va_get_reg64 rR14 va_s0) (va_get_reg64 rR11 va_s0) < va_mul_nat n (n
`op_Division` 16) /\ va_mul_nat (va_get_reg64 rRbx va_s0) (va_get_reg64 rR13 va_s0) <
va_mul_nat n (n `op_Division` 8) /\ va_mul_nat (va_get_reg64 rRbp va_s0) (va_get_reg64 rR13
va_s0) < 7 `op_Multiply` (5 `op_Multiply` n `op_Division` 64) /\ va_get_reg64 rRax va_s0 == r1)
/\ (forall (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_efl:Vale.X64.Flags.t) (hh:int) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14
(va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 va_s0))))))))
in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rR10 va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p /\
va_get_reg64 rR10 va_sM `op_Division` 4 `op_Multiply` 4 + va_get_reg64 rR10 va_sM `op_Division`
4 < 18446744073709551616 /\ va_get_reg64 rRax va_sM == 18446744073709551612) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_multiply : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_multiply r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_multiply ()) ([va_Mod_flags;
va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_multiply r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_multiply (va_code_Poly1305_multiply ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRdx va_sM (va_update_reg64
rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok
va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_multiply (r1:nat64) : (va_quickCode int (va_code_Poly1305_multiply ())) =
(va_QProc (va_code_Poly1305_multiply ()) ([va_Mod_flags; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8]) (va_wp_Poly1305_multiply r1) (va_wpProof_Poly1305_multiply r1))
//--
//-- Poly1305_reduce
val va_code_Poly1305_reduce : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce () =
(va_Block (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_CCons
(va_code_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))
val va_codegen_success_Poly1305_reduce : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce () =
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_ttrue ())))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce (va_mods:va_mods_t) : (va_quickCode (int) (va_code_Poly1305_reduce
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s) + va_mul_nat n (va_get_reg64 rRbx va_s) + va_get_reg64 rR14 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 164 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 166 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 167 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 168 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 169 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 170 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 171 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 172 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 173 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
let (h10:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat n (va_get_reg64
rRbx va_old_s) + va_get_reg64 rR14 va_old_s in let (hh:int) = h10 + va_get_reg64 rRax va_s +
va_mul_nat (va_get_reg64 rR10 va_old_s `op_Modulus` 4) (va_mul_nat n n) in let
(va_arg27:Prims.int) = hh in let (va_arg26:Prims.int) = va_get_reg64 rRax va_s in let
(va_arg25:Prims.int) = h10 in let (va_arg24:Prims.int) = va_get_reg64 rR10 va_old_s in let
(va_arg23:Prims.int) = hd in let (va_arg22:Prims.int) = p in let (va_arg21:Prims.int) = n in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 177 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_reduce va_arg21 va_arg22 va_arg23 va_arg24
va_arg25 va_arg26 va_arg27) (va_QEmpty ((hh))))))))))))))
val va_lemma_Poly1305_reduce : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 ==
18446744073709551612)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh
`op_Modulus` p /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 147 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in label va_range1
"***** POSTCONDITION NOT MET AT line 160 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 161 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hd `op_Modulus` p == hh `op_Modulus` p) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 162 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_reduce (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(hd:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_mul_nat n n) (va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) +
va_get_reg64 rR14 va_s0 in va_get_reg64 rR10 va_s0 `op_Division` 4 `op_Multiply` 4 +
va_get_reg64 rR10 va_s0 `op_Division` 4 < n /\ va_get_reg64 rRax va_s0 == 18446744073709551612)
/\ (forall (va_x_rax:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rRax va_x_rax va_s0))))) in va_get_ok va_sM /\ (let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (hd:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_mul_nat n n)
(va_get_reg64 rR10 va_s0) + va_mul_nat n (va_get_reg64 rRbx va_s0) + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ hd `op_Modulus` p == hh `op_Modulus` p /\ va_get_reg64 rRbp
va_sM < 5) ==> va_k va_sM ((hh))))
val va_wpProof_Poly1305_reduce : va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_reduce (va_code_Poly1305_reduce ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce () : (va_quickCode int (va_code_Poly1305_reduce ())) =
(va_QProc (va_code_Poly1305_reduce ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rRax]) va_wp_Poly1305_reduce
va_wpProof_Poly1305_reduce)
//--
//-- Poly1305_iteration
val va_code_Poly1305_iteration : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_iteration () =
(va_Block (va_CCons (va_code_Poly1305_multiply ()) (va_CCons (va_code_Poly1305_reduce ())
(va_CNil ()))))
val va_codegen_success_Poly1305_iteration : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_iteration () =
(va_pbool_and (va_codegen_success_Poly1305_multiply ()) (va_pbool_and
(va_codegen_success_Poly1305_reduce ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_iteration (va_mods:va_mods_t) (r1:nat64) : (va_quickCode (int)
(va_code_Poly1305_iteration ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s) n +
va_get_reg64 rR14 va_s in let (va_arg50:Prims.int) = n `op_Division` 16 in let
(va_arg49:Prims.int) = va_get_reg64 rR11 va_s in let (va_arg48:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 210 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg48 7 va_arg49 va_arg50)
(let (va_arg47:Prims.int) = n `op_Division` 16 in let (va_arg46:Prims.int) = r1 in let
(va_arg45:Prims.int) = n in let (va_arg44:Prims.int) = va_get_reg64 rR14 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 211 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg44 va_arg45 va_arg46
va_arg47) (let (va_arg43:Prims.int) = n `op_Division` 16 in let (va_arg42:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg41:Prims.int) = n in let (va_arg40:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 212 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg40 va_arg41 va_arg42
va_arg43) (let (va_arg39:Prims.int) = n `op_Division` 8 in let (va_arg38:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg37:Prims.int) = n in let (va_arg36:Prims.int) =
va_get_reg64 rRbp va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 213 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg36 va_arg37 va_arg38
va_arg39) (let (va_arg35:Prims.int) = n `op_Division` 16 in let (va_arg34:Prims.int) =
va_get_reg64 rR11 va_s in let (va_arg33:Prims.int) = n in let (va_arg32:Prims.int) =
va_get_reg64 rR14 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 214 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg32 va_arg33 va_arg34
va_arg35) (let (va_arg31:Prims.int) = n `op_Division` 8 in let (va_arg30:Prims.int) =
va_get_reg64 rR13 va_s in let (va_arg29:Prims.int) = n in let (va_arg28:Prims.int) =
va_get_reg64 rRbx va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 215 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg28 va_arg29 va_arg30
va_arg31) (let (va_arg27:Prims.int) = 5 `op_Multiply` n `op_Division` 64 in let
(va_arg26:Prims.int) = va_get_reg64 rR13 va_s in let (va_arg25:Prims.int) = va_get_reg64 rRbp
va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 216 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mul_strict_upper_bound va_arg25 7 va_arg26 va_arg27)
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 218 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_multiply r1) (fun (va_s:va_state) (hd:int) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 219 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce ()) (fun (va_s:va_state) (hh:int) -> va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 220 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 221 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(l_and (hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_s) + va_mul_nat n (va_get_reg64
rRbx va_s) + va_get_reg64 rR14 va_s) (va_mul_nat h r `op_Modulus` p == hh `op_Modulus` p))
(va_QEmpty ((hh)))))))))))))))
val va_lemma_Poly1305_iteration : va_b0:va_code -> va_s0:va_state -> r1:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_iteration ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1)))
(ensures (fun (va_sM, va_fM, hh) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp (va_mul_nat h r) ==
Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_iteration va_b0 va_s0 r1 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok] in
let va_qc = va_qcode_Poly1305_iteration va_mods r1 in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_iteration ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let hh = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 180 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
label va_range1
"***** POSTCONDITION NOT MET AT line 200 column 41 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) + va_mul_nat n (va_get_reg64 rRbx
va_sM) + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 201 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp (va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 202 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax;
va_Mod_ok]) va_sM va_s0;
let hh = va_g in
(va_sM, va_fM, hh)
[@ va_qattr]
let va_wp_Poly1305_iteration (r1:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r:(va_int_range 0 340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64
rR11 va_s0 in let (h:(va_int_range 0
6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat (va_get_reg64 rRbp
va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n + va_get_reg64 rR14 va_s0 in
va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n `op_Division` 16 /\ r1 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division` 4 /\ va_get_reg64 rRbp va_s0 < 7 /\
va_get_reg64 rRax va_s0 == r1) /\ (forall (va_x_rax:nat64) (va_x_rdx:nat64) (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64)
(va_x_efl:Vale.X64.Flags.t) (hh:int) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp
va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRax va_x_rax va_s0)))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r:(va_int_range 0
340282366920938463463374607431768211455)) = va_mul_nat r1 n + va_get_reg64 rR11 va_s0 in let
(h:(va_int_range 0 6277101735386680763835789423207666416102355444464034512895)) = va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx va_s0) n +
va_get_reg64 rR14 va_s0 in hh == va_mul_nat (va_mul_nat n n) (va_get_reg64 rRbp va_sM) +
va_mul_nat n (va_get_reg64 rRbx va_sM) + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp
(va_mul_nat h r) == Vale.Poly1305.Spec_s.modp hh /\ va_get_reg64 rRbp va_sM < 5) ==> va_k va_sM
((hh))))
val va_wpProof_Poly1305_iteration : r1:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_iteration r1 va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_iteration ()) ([va_Mod_flags;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_iteration r1 va_s0 va_k =
let (va_sM, va_f0, hh) = va_lemma_Poly1305_iteration (va_code_Poly1305_iteration ()) va_s0 r1 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRax])
va_sM va_s0;
let va_g = (hh) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_iteration (r1:nat64) : (va_quickCode int (va_code_Poly1305_iteration ())) =
(va_QProc (va_code_Poly1305_iteration ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRax]) (va_wp_Poly1305_iteration r1) (va_wpProof_Poly1305_iteration r1))
//--
//-- Poly1305_blocks_body0
val va_code_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_body0 () =
(va_Block (va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 Public))
(va_CCons (va_code_Mem64_lemma ()) (va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_CCons
(va_code_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (va_CCons
(va_code_Poly1305_iteration ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64
1)) (va_CNil ())))))))))))
val va_codegen_success_Poly1305_blocks_body0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_body0 () =
(va_pbool_and (va_codegen_success_Mem64_lemma ()) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet 0)
(va_op_reg64_reg64 rRsi) 0 Public)) (va_pbool_and (va_codegen_success_Mem64_lemma ())
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64
(va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_pbool_and
(va_codegen_success_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi)
(va_const_opr64 16)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Poly1305_iteration ())
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1))
(va_ttrue ()))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_body0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_body0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in let (nn:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (hp:int) = h in let (h:int) = h +
va_mul_nat (va_mul_nat nn nn) (va_get_reg64 rRcx va_s) + va_mul_nat nn
(Vale.X64.Decls.buffer64_read inp_b (word_index + 1) (va_get_mem_heaplet 0 va_s)) +
Vale.X64.Decls.buffer64_read inp_b word_index (va_get_mem_heaplet 0 va_s) in let (hq:int) = h
in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 0 inp_b word_index
Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 353 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 0 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mem64_lemma (va_op_heaplet_mem_heaplet 0) (va_op_reg64_reg64 rRsi) 8 inp_b
(word_index + 1) Public) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 354 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_opr_code_Mem64 (va_op_heaplet_mem_heaplet
0) (va_op_reg64_reg64 rRsi) 8 Public)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 355 column 17 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_AddLea64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRsi) (va_const_opr64 16))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 356 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state)
_ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 358 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hq == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat nn nn) + va_mul_nat (va_get_reg64 rRbx
va_s) nn + va_get_reg64 rR14 va_s) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 360 column 11 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration (va_get_reg64 rR12 va_s)) (fun (va_s:va_state) (h:int) -> va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 362 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 363 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rR15) (va_const_opr64 1)) (fun (va_s:va_state) _ -> let
(word_index:nat) = word_index + 2 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 366 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index) (let
(va_arg50:Prims.int) = word_index in let (va_arg49:(FStar.Seq.Base.seq Vale.X64.Memory.nat64))
= Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b in let (va_arg48:Prims.int)
= r in let (va_arg47:Prims.int) = va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let
(va_arg46:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 368 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg46 va_arg47 va_arg48
va_arg49 va_arg50) (let (va_arg45:Prims.int) = word_index - 2 in let
(va_arg44:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg43:Prims.int) = r in let (va_arg42:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat nn nn) in let (va_arg41:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 369 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg41 va_arg42 va_arg43
va_arg44 va_arg45) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 370 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:Prims.int) = r in let (va_arg39:Prims.int) = hq - hp in let (va_arg38:Prims.int) = hp
in let (va_arg37:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 371 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg37 va_arg38 va_arg39 va_arg40)
(va_QEmpty (())))))) (va_QEmpty ((h, word_index)))))))))))))))
val va_lemma_Poly1305_blocks_body0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_body0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old /\ va_get_reg64 rR15 va_s0 =!= 0))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15
va_s0) /\ va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_body0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_body0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_body0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 345 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
va_get_reg64 rR15 va_s0 =!= 0 /\ (forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_rax:nat64) (va_x_rbp:nat64) (va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int)
(word_index:nat) . let va_sM = va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64
rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_ok va_x_ok (va_upd_flags va_x_efl
va_s0))))))))))) in va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n ==
va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\
va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h ==
va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64
rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12
va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64
rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM ==
va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM
== va_get_reg64 rRsi va_old + va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64
/\ va_in_length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8
`op_Multiply` (word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8
`op_Multiply` word_index == va_in_length /\ va_get_reg64 rRsi va_sM + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) +
8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_sM < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old /\
precedes_wrap (va_get_reg64 rR15 va_sM) (va_get_reg64 rR15 va_s0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_body0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int ->
va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_body0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_body0 (va_code_Poly1305_blocks_body0
()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r
va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_body0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_body0 ())) =
(va_QProc (va_code_Poly1305_blocks_body0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64
rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_body0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_body0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks_while0
val va_code_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks_while0 () =
(va_Block (va_CCons (va_While (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Poly1305_blocks_body0 ()) (va_CNil ())))) (va_CNil ())))
val va_codegen_success_Poly1305_blocks_while0 : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks_while0 () =
(va_pbool_and (va_codegen_success_Poly1305_blocks_body0 ()) (va_ttrue ()))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks_while0 (va_mods:va_mods_t) (va_old:va_state) (va_in_ctx_b:buffer64)
(va_in_h_in:int) (va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range
18446744073709551616 18446744073709551616)) (va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) (va_in_r:int)
(va_in_h:int) (va_in_word_index:nat) : (va_quickCode (int & nat) (va_code_Poly1305_blocks_while0
())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (ctx_b:buffer64) =
va_in_ctx_b in let (h_in:int) = va_in_h_in in let (inp_b:buffer64) = va_in_inp_b in let
(length:int) = va_in_length in let (n:(va_int_range 18446744073709551616 18446744073709551616))
= va_in_n in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_in_p in let (r:int) = va_in_r in let (h:int) =
va_in_h in let (word_index:nat) = va_in_word_index in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qWhile va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (fun va_g -> let (h:int) =
let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g in
word_index in qblock va_mods (fun (va_s:va_state) -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_body0 va_old ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QEmpty ((h, word_index))))) (fun
(va_s:va_state) va_g -> let (h:int) = let (h, word_index) = va_g in h in let (word_index:nat) =
let (h, word_index) = va_g in word_index in va_get_ok va_s /\ n == pow2_64 /\ va_mul_nat n n ==
va_mul_nat pow2_64 pow2_64 /\ p == va_mul_nat n n `op_Multiply` 4 - 5 /\ r == va_mul_nat
(va_get_reg64 rR12 va_s) n + va_get_reg64 rR11 va_s /\ h == va_mul_nat (va_get_reg64 rRbp va_s)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s) pow2_64 + va_get_reg64 rR14
va_s /\ va_get_reg64 rR11 va_s < n `op_Division` 16 /\ va_get_reg64 rR12 va_s < n `op_Division`
16 /\ va_get_reg64 rR12 va_s `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s == va_get_reg64 rR12
va_s + va_get_reg64 rR12 va_s `op_Division` 4 /\ va_get_reg64 rRbp va_s < 5 /\ va_get_reg64
rRax va_s == va_get_reg64 rR12 va_s /\ va_get_reg64 rRsi va_s + 16 `op_Multiply` va_get_reg64
rR15 va_s == va_get_reg64 rRsi va_old + length /\ va_get_reg64 rRsi va_old + length < pow2_64
/\ length == va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s =!= 0 ==> 8 `op_Multiply`
(word_index + 1) <= length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s + 8 `op_Multiply`
word_index == length /\ va_get_reg64 rRsi va_s + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 inp_b (va_get_mem_heaplet 0 va_s) + 8 `op_Multiply` word_index /\
va_get_reg64 rR15 va_s `op_Multiply` 16 <= length /\ va_get_reg64 rRcx va_s < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s) (va_get_reg64 rRdi va_s) ctx_b 24
(va_get_mem_layout va_s) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s)
(va_get_reg64 rRsi va_old) inp_b (length `op_Division` 8) (va_get_mem_layout va_s) Public /\
va_get_reg64 rRdi va_s == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s == va_get_reg64
rRcx va_old /\ (va_get_reg64 rRsi va_s - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) word_index /\
va_get_mem_heaplet 1 va_s == va_get_mem_heaplet 1 va_old) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in va_get_reg64 rR15 va_s) ((h, word_index))) (fun (va_s:va_state) va_g -> let
(h:int) = let (h, word_index) = va_g in h in let (word_index:nat) = let (h, word_index) = va_g
in word_index in let va_g = (h, word_index) in let ((h:int), (word_index:nat)) = va_g in
va_QEmpty ((h, word_index)))))
val va_lemma_Poly1305_blocks_while0 : va_b0:va_code -> va_s0:va_state -> va_old:va_state ->
va_in_ctx_b:buffer64 -> va_in_h_in:int -> va_in_inp_b:buffer64 -> va_in_length:int ->
va_in_n:(va_int_range 18446744073709551616 18446744073709551616) -> va_in_p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819) -> va_in_r:int
-> va_in_h:int -> va_in_word_index:nat
-> Ghost (va_state & va_fuel & int & nat)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks_while0 ()) va_s0 /\ va_get_ok va_s0 /\
va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p ==
va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12
va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat (va_get_reg64 rRbp va_s0)
(va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0) pow2_64 + va_get_reg64 rR14
va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 <
va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13
va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division` 4 /\ va_get_reg64 rRbp
va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\ va_get_reg64 rRsi va_s0 + 16
`op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply` (va_in_word_index + 1) <= va_in_length)
/\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8 `op_Multiply` va_in_word_index == va_in_length
/\ va_get_reg64 rRsi va_s0 + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_s0) + 8 `op_Multiply` va_in_word_index /\ va_get_reg64
rR15 va_s0 `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_s0 < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0)
va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRdi va_s0 == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_s0 - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp va_in_h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_s0) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s0) va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 ==
va_get_mem_heaplet 1 va_old))
(ensures (fun (va_sM, va_fM, h, word_index) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\
va_get_ok va_sM /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64
rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 +
va_get_reg64 rR14 va_sM /\ va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64
rR12 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\
va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\
va_get_reg64 rRbp va_sM < 5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\
va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1)
<= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index ==
va_in_length /\ va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr
#Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index
/\ va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) /\ va_state_eq va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM
(va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags va_sM va_s0))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks_while0 va_b0 va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index =
let va_old = va_expand_state va_old in
let (va_mods:va_mods_t) = [va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64
rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags] in
let va_qc = va_qcode_Poly1305_blocks_while0 va_mods va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks_while0 ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let (h, word_index) = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 317 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_n == pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 318 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 319 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 320 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n + va_get_reg64 rR11 va_sM) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 321 column 62 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 322 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 323 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM < va_in_n `op_Division` 16) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 324 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 325 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 326 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 327 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 328 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 16 `op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old
+ va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 329 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_old + va_in_length < pow2_64) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 330 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_in_length == va_get_reg64 rRdx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 332 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 333 column 48 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(16 `op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length) /\
label va_range1
"***** POSTCONDITION NOT MET AT line 334 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64
va_in_inp_b (va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 336 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_sM `op_Multiply` 16 <= va_in_length) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 337 column 23 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM < 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 338 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 339 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 340 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 341 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 342 column 39 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
((va_get_reg64 rRsi va_sM - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 343 column 120 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM)
va_in_inp_b) word_index) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 344 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_mem_heaplet 1 va_sM == va_get_mem_heaplet 1 va_old) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(~(va_get_reg64 rR15 va_sM =!= 0))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let (h, word_index) = va_g in
(va_sM, va_fM, h, word_index)
[@ va_qattr]
let va_wp_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat)
(va_s0:va_state) (va_k:(va_state -> (int & nat) -> Type0)) : Type0 =
(va_get_ok va_s0 /\ va_in_n == pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64
pow2_64 /\ va_in_p == va_mul_nat va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat
(va_get_reg64 rR12 va_s0) va_in_n + va_get_reg64 rR11 va_s0 /\ va_in_h == va_mul_nat
(va_get_reg64 rRbp va_s0) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_s0)
pow2_64 + va_get_reg64 rR14 va_s0 /\ va_get_reg64 rR11 va_s0 < va_in_n `op_Division` 16 /\
va_get_reg64 rR12 va_s0 < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_s0 `op_Modulus` 4 ==
0 /\ va_get_reg64 rR13 va_s0 == va_get_reg64 rR12 va_s0 + va_get_reg64 rR12 va_s0 `op_Division`
4 /\ va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rRax va_s0 == va_get_reg64 rR12 va_s0 /\
va_get_reg64 rRsi va_s0 + 16 `op_Multiply` va_get_reg64 rR15 va_s0 == va_get_reg64 rRsi va_old
+ va_in_length /\ va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length ==
va_get_reg64 rRdx va_old /\ (va_get_reg64 rR15 va_s0 =!= 0 ==> 8 `op_Multiply`
(va_in_word_index + 1) <= va_in_length) /\ 16 `op_Multiply` va_get_reg64 rR15 va_s0 + 8
`op_Multiply` va_in_word_index == va_in_length /\ va_get_reg64 rRsi va_s0 + 0 ==
Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b (va_get_mem_heaplet 0 va_s0) +
8 `op_Multiply` va_in_word_index /\ va_get_reg64 rR15 va_s0 `op_Multiply` 16 <= va_in_length /\
va_get_reg64 rRcx va_s0 < 2 /\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0)
(va_get_reg64 rRdi va_s0) va_in_ctx_b 24 (va_get_mem_layout va_s0) Public /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_old)
va_in_inp_b (va_in_length `op_Division` 8) (va_get_mem_layout va_s0) Public /\ va_get_reg64
rRdi va_s0 == va_get_reg64 rRdi va_old /\ va_get_reg64 rRcx va_s0 == va_get_reg64 rRcx va_old
/\ (va_get_reg64 rRsi va_s0 - va_get_reg64 rRsi va_old) `op_Modulus` 16 == 0 /\
Vale.Poly1305.Spec_s.modp va_in_h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat (va_get_reg64 rRcx va_s0) (va_mul_nat
va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s0)
va_in_inp_b) va_in_word_index /\ va_get_mem_heaplet 1 va_s0 == va_get_mem_heaplet 1 va_old /\
(forall (va_x_efl:Vale.X64.Flags.t) (va_x_ok:bool) (va_x_r10:nat64) (va_x_r14:nat64)
(va_x_r15:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_rax:nat64) (va_x_rbp:nat64)
(va_x_rbx:nat64) (va_x_rdx:nat64) (va_x_rsi:nat64) (h:int) (word_index:nat) . let va_sM =
va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10
(va_upd_ok va_x_ok (va_upd_flags va_x_efl va_s0))))))))))) in va_get_ok va_sM /\ va_in_n ==
pow2_64 /\ va_mul_nat va_in_n va_in_n == va_mul_nat pow2_64 pow2_64 /\ va_in_p == va_mul_nat
va_in_n va_in_n `op_Multiply` 4 - 5 /\ va_in_r == va_mul_nat (va_get_reg64 rR12 va_sM) va_in_n
+ va_get_reg64 rR11 va_sM /\ h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
va_get_reg64 rR11 va_sM < va_in_n `op_Division` 16 /\ va_get_reg64 rR12 va_sM < va_in_n
`op_Division` 16 /\ va_get_reg64 rR12 va_sM `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_sM ==
va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRbp va_sM <
5 /\ va_get_reg64 rRax va_sM == va_get_reg64 rR12 va_sM /\ va_get_reg64 rRsi va_sM + 16
`op_Multiply` va_get_reg64 rR15 va_sM == va_get_reg64 rRsi va_old + va_in_length /\
va_get_reg64 rRsi va_old + va_in_length < pow2_64 /\ va_in_length == va_get_reg64 rRdx va_old
/\ (va_get_reg64 rR15 va_sM =!= 0 ==> 8 `op_Multiply` (word_index + 1) <= va_in_length) /\ 16
`op_Multiply` va_get_reg64 rR15 va_sM + 8 `op_Multiply` word_index == va_in_length /\
va_get_reg64 rRsi va_sM + 0 == Vale.X64.Memory.buffer_addr #Vale.X64.Memory.vuint64 va_in_inp_b
(va_get_mem_heaplet 0 va_sM) + 8 `op_Multiply` word_index /\ va_get_reg64 rR15 va_sM
`op_Multiply` 16 <= va_in_length /\ va_get_reg64 rRcx va_sM < 2 /\
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM)
va_in_ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_old) va_in_inp_b (va_in_length `op_Division`
8) (va_get_mem_layout va_sM) Public /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_old /\
va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_old /\ (va_get_reg64 rRsi va_sM - va_get_reg64
rRsi va_old) `op_Modulus` 16 == 0 /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp va_in_h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat va_in_n va_in_n)) va_in_r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) va_in_inp_b) word_index /\ va_get_mem_heaplet 1 va_sM ==
va_get_mem_heaplet 1 va_old /\ ~(va_get_reg64 rR15 va_sM =!= 0) ==> va_k va_sM ((h,
word_index))))
val va_wpProof_Poly1305_blocks_while0 : va_old:va_state -> va_in_ctx_b:buffer64 -> va_in_h_in:int
-> va_in_inp_b:buffer64 -> va_in_length:int -> va_in_n:(va_int_range 18446744073709551616
18446744073709551616) -> va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) -> va_in_r:int -> va_in_h:int -> va_in_word_index:nat
-> va_s0:va_state -> va_k:(va_state -> (int & nat) -> Type0)
-> Ghost (va_state & va_fuel & (int & nat))
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in
va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks_while0 ())
([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64
rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64
rR10; va_Mod_ok; va_Mod_flags]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length
va_in_n va_in_p va_in_r va_in_h va_in_word_index va_s0 va_k =
let (va_sM, va_f0, h, word_index) = va_lemma_Poly1305_blocks_while0
(va_code_Poly1305_blocks_while0 ()) va_s0 va_old va_in_ctx_b va_in_h_in va_in_inp_b
va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRax va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_ok va_sM (va_update_flags
va_sM va_s0)))))))))))));
va_lemma_norm_mods ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx; va_Mod_reg64 rRbx; va_Mod_reg64 rRbp;
va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags]) va_sM va_s0;
let va_g = (h, word_index) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks_while0 (va_old:va_state) (va_in_ctx_b:buffer64) (va_in_h_in:int)
(va_in_inp_b:buffer64) (va_in_length:int) (va_in_n:(va_int_range 18446744073709551616
18446744073709551616)) (va_in_p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) (va_in_r:int) (va_in_h:int) (va_in_word_index:nat) :
(va_quickCode (int & nat) (va_code_Poly1305_blocks_while0 ())) =
(va_QProc (va_code_Poly1305_blocks_while0 ()) ([va_Mod_reg64 rRsi; va_Mod_reg64 rRdx;
va_Mod_reg64 rRbx; va_Mod_reg64 rRbp; va_Mod_reg64 rRax; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_ok; va_Mod_flags])
(va_wp_Poly1305_blocks_while0 va_old va_in_ctx_b va_in_h_in va_in_inp_b va_in_length va_in_n
va_in_p va_in_r va_in_h va_in_word_index) (va_wpProof_Poly1305_blocks_while0 va_old va_in_ctx_b
va_in_h_in va_in_inp_b va_in_length va_in_n va_in_p va_in_r va_in_h va_in_word_index))
//--
//-- Poly1305_blocks
val va_code_Poly1305_blocks : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_blocks () =
(va_Block (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR14) (va_op_reg_opr64_reg64 rRdi) 0 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rRbp) (va_op_reg_opr64_reg64 rRdi) 16 Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rR12) (va_op_opr64_reg64 rR13)) (va_CCons (va_code_Shr64 (va_op_dst_opr64_reg64 rR13)
(va_const_shift_amt64 2)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Add64 (va_op_dst_opr64_reg64 rR13)
(va_op_opr64_reg64 rR12)) (va_CCons (va_code_Poly1305_blocks_while0 ()) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbp) 16 Public) (va_CNil ())))))))))))))))))
val va_codegen_success_Poly1305_blocks : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_blocks () =
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14) (va_op_reg_opr64_reg64 rRdi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRbx) (va_op_reg_opr64_reg64 rRdi) 8 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Shr64
(va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Add64
(va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Poly1305_blocks_while0 ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_ttrue ()))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_blocks (va_mods:va_mods_t) (r:int) (h_in:int) (ctx_b:buffer64)
(inp_b:buffer64) : (va_quickCode (int) (va_code_Poly1305_blocks ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 285 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (let (length:int) = va_get_reg64 rRdx
va_s in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 289 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rRdx) (va_const_shift_amt64 4)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 292 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR15) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 294 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 295 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR13)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 297 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR14)
(va_op_reg_opr64_reg64 rRdi) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 298 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbx)
(va_op_reg_opr64_reg64 rRdi) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 299 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRbp)
(va_op_reg_opr64_reg64 rRdi) 16 Public ctx_b 2) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 301 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rR13)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 302 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR13) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 303 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR12)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 304 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR13) (va_op_opr64_reg64 rR12)) (fun (va_s:va_state) _
-> let (h:int) = h_in in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 307 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) 0) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 309 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp) (let
(va_arg40:(FStar.Seq.Base.seq Vale.X64.Memory.nat64)) = Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_s) inp_b in let (va_arg39:Prims.int) = r in let (va_arg38:Prims.int) =
va_mul_nat (va_get_reg64 rRcx va_s) (va_mul_nat n n) in let (va_arg37:Prims.int) =
Vale.Poly1305.Spec_s.modp h_in in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 310 column 36 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.reveal_poly1305_heap_blocks va_arg37 va_arg38 va_arg39
va_arg40 0) (va_QEmpty (())))) (let (word_index:nat) = 0 in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 315 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks_while0 va_old_s ctx_b h_in inp_b length n p r h word_index) (fun
(va_s:va_state) va_g -> let (h, word_index) = va_g in va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 374 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR14) 0 Public ctx_b 0) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 375 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbx) 8 Public ctx_b 1) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 376 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public ctx_b 2) (va_QEmpty ((h)))))))))))))))))))))
val va_lemma_Poly1305_blocks : va_b0:va_code -> va_s0:va_state -> r:int -> h_in:int ->
ctx_b:buffer64 -> inp_b:buffer64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_blocks ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRdx va_s0 `op_Modulus` 16 == 0 /\
va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64 /\ Vale.X64.Decls.validDstAddrs64
(va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24 (va_get_mem_layout va_s0)
Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0) (va_get_reg64 rRsi va_s0)
inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_s0) Public /\ (let h0_in
= Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in
(va_mul_nat n n) + va_mul_nat h1_in n + h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n
`op_Division` 16 /\ r1_in < n `op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\
va_get_reg64 rRcx va_s0 < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRbp va_sM < 5 /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64
rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64
(va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0
`op_Division` 8) (va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific
ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM
== Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM
== Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM
== Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM
== va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM
== va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64
rRcx va_s0 /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in let r1_in =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in h == va_mul_nat
(va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM)
pow2_64 + va_get_reg64 rR14 va_sM /\ Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Util.poly1305_heap_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat
(va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r (Vale.X64.Decls.buffer64_as_seq
(va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0 `op_Division` 8))) /\ va_state_eq
va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64 rR15 va_sM
(va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_blocks va_b0 va_s0 r h_in ctx_b inp_b =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64
rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64
rRdx; va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_blocks va_mods r h_in ctx_b inp_b in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_blocks ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 224 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in label
va_range1
"***** POSTCONDITION NOT MET AT line 264 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 265 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 266 column 79 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM) (va_get_reg64 rRsi va_s0) inp_b
(va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 267 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 2) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 268 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 269 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 270 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 271 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 272 column 45 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM))
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 273 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM + va_get_reg64 rR12 va_sM `op_Division` 4)
/\ label va_range1
"***** POSTCONDITION NOT MET AT line 274 column 30 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 277 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 278 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 280 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 281 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_sM) in label
va_range1
"***** POSTCONDITION NOT MET AT line 282 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64 pow2_64) + va_mul_nat
(va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 283 column 118 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) (va_s0:va_state)
(va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64
rRdx va_s0 `op_Modulus` 16 == 0 /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8)
(va_get_mem_layout va_s0) Public /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0
(va_get_mem_heaplet 1 va_s0) in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1
(va_get_mem_heaplet 1 va_s0) in let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s0) in let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_s0) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_s0) in h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n
+ h0_in /\ r == va_mul_nat r1_in n + r0_in /\ r0_in < n `op_Division` 16 /\ r1_in < n
`op_Division` 16 /\ r1_in `op_Modulus` 4 == 0 /\ h2_in < 5 /\ va_get_reg64 rRcx va_s0 < 2)) /\
(forall (va_x_mem:vale_heap) (va_x_rsi:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r11:nat64) (va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64)
(va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_rax:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rRax va_x_rax (va_upd_reg64 rRbp va_x_rbp
(va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64
rRsi va_x_rsi (va_upd_mem va_x_mem va_s0))))))))))))))) in va_get_ok va_sM /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in va_get_reg64 rRbp va_sM < 5 /\
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_sM)
(va_get_reg64 rRsi va_s0) inp_b (va_get_reg64 rRdx va_s0 `op_Division` 8) (va_get_mem_layout
va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0)
(va_get_mem_heaplet 1 va_sM) 0 2 /\ va_get_reg64 rR14 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 0 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbx va_sM == Vale.X64.Decls.buffer64_read
ctx_b 1 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rRbp va_sM == Vale.X64.Decls.buffer64_read
ctx_b 2 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR11 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 3 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR12 va_sM == Vale.X64.Decls.buffer64_read
ctx_b 4 (va_get_mem_heaplet 1 va_sM) /\ va_get_reg64 rR13 va_sM == va_get_reg64 rR12 va_sM +
va_get_reg64 rR12 va_sM `op_Division` 4 /\ va_get_reg64 rRsi va_sM == va_get_reg64 rRsi va_s0 +
va_get_reg64 rRdx va_s0 /\ va_get_reg64 rRcx va_sM == va_get_reg64 rRcx va_s0 /\ va_get_reg64
rRdi va_sM == va_get_reg64 rRdi va_s0 /\ (let r0_in = Vale.X64.Decls.buffer64_read ctx_b 3
(va_get_mem_heaplet 1 va_sM) in let r1_in = Vale.X64.Decls.buffer64_read ctx_b 4
(va_get_mem_heaplet 1 va_sM) in h == va_mul_nat (va_get_reg64 rRbp va_sM) (va_mul_nat pow2_64
pow2_64) + va_mul_nat (va_get_reg64 rRbx va_sM) pow2_64 + va_get_reg64 rR14 va_sM /\
Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Util.poly1305_heap_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat (va_get_reg64 rRcx va_sM) (va_mul_nat n n)) r
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_sM) inp_b) (va_get_reg64 rRdx va_s0
`op_Division` 8))) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_blocks : r:int -> h_in:int -> ctx_b:buffer64 -> inp_b:buffer64 ->
va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_blocks ())
([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRsi;
va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_blocks r h_in ctx_b inp_b va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_blocks (va_code_Poly1305_blocks ()) va_s0 r h_in ctx_b
inp_b in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRsi va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rRax;
va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRsi; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_blocks (r:int) (h_in:int) (ctx_b:buffer64) (inp_b:buffer64) : (va_quickCode
int (va_code_Poly1305_blocks ())) =
(va_QProc (va_code_Poly1305_blocks ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rRax; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR13;
va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8;
va_Mod_reg64 rRdx; va_Mod_reg64 rRsi; va_Mod_mem]) (va_wp_Poly1305_blocks r h_in ctx_b inp_b)
(va_wpProof_Poly1305_blocks r h_in ctx_b inp_b))
//--
//-- Poly1305_last_block
val va_code_Poly1305_last_block : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_last_block () =
(va_Block (va_CCons (va_IfElse (va_cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (va_Block
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_CCons
(va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Sub64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ())))))))))))))))) (va_Block
(va_CCons (va_Block (va_CNil ())) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_CCons (va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
8)) (va_CCons (va_code_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_CCons (va_code_Shl64
(va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (va_CCons (va_Block (va_CNil ()))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CCons (va_code_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_CNil ()))))))))))))))))))) (va_CCons
(va_code_Poly1305_iteration ()) (va_CNil ()))))
val va_codegen_success_Poly1305_last_block : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_last_block () =
(va_pbool_and (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx)
(va_const_shift_amt64 3)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_const_opr64 1)) (va_pbool_and (va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx)
(va_op_shift_amt64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRcx) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64
rRcx) (va_const_opr64 1)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8)
(va_op_opr64_reg64 rRcx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9)
(va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14)
(va_op_opr64_reg64 rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap
(va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_pbool_and
(va_codegen_success_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx))
(va_pbool_and (va_codegen_success_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rR9)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbp) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64
rR14) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64
rRbx) (va_op_opr64_reg64 rRdx)) (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbp)
(va_const_opr64 0))))))))))))))))))))))))))))) (va_pbool_and
(va_codegen_success_Poly1305_iteration ()) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_last_block (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_last_block ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s)
(va_get_reg64 rR9 va_s) in let (padLast:Prims.pos) = Prims.pow2 (va_get_reg64 rR15 va_s
`op_Multiply` 8) in va_QBind va_range1
"***** PRECONDITION NOT MET AT line 409 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_lt (va_op_cmp_reg64 rR15) (va_const_cmp 8)) (qblock va_mods (fun
(va_s:va_state) -> let (va_arg78:Vale.Def.Types_s.nat64) = va_get_reg64 rR15 va_s in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 410 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg78) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 411 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 412 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 413 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 414 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 415 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdx va_s == padLast) (let (va_arg77:Vale.Def.Types_s.nat64) = va_get_reg64 rR15
va_s in let (va_arg76:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 417 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg76 va_arg77) (va_qAssert
va_range1
"***** PRECONDITION NOT MET AT line 419 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.shift_left64 1 (Vale.Poly1305.Math.shift_left64 (va_get_reg64
rR15 va_s) 3)) (let (va_arg75:Prims.int) = Prims.pow2 (va_get_reg64 rR15 va_s `op_Multiply` 8)
in let (va_arg74:Prims.int) = va_get_reg64 rR15 va_s in let (va_arg73:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in let (va_arg72:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 420 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_power2_lo va_arg72 va_arg73 va_arg74 va_arg75)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 421 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 422 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 423 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRcx)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 424 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 425 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR8 va_s == va_get_reg64 rR8 va_old_s `op_Modulus` padLast) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 426 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 429 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 430 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 431 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 433 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 434 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 435 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(())))))))))))))))))))))))) (qblock va_mods (fun (va_s:va_state) -> va_qAssertSquash va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 437 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rR15 va_s - 8 >= 0 /\ va_get_reg64 rR15 va_s - 8 <= 255) (fun _ -> let
(nExtra8:nat8) = va_get_reg64 rR15 va_s - 8 in let (va_arg85:Vale.Def.Types_s.nat64) = nExtra8
in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 438 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_shift_power2 va_arg85) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 439 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 440 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 441 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRcx) (va_const_shift_amt64 3)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 442 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 443 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shl64 (va_op_dst_opr64_reg64 rRdx) (va_op_shift_amt64_reg64 rRcx)) (fun
(va_s:va_state) _ -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 445 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(padLast == Vale.Poly1305.Math.lowerUpper128 0 (va_get_reg64 rRdx va_s)) (let
(va_arg84:Prims.nat) = 8 `op_Multiply` nExtra8 in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 446 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_power2_add64 va_arg84) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 447 column 33 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg83:Vale.Def.Types_s.nat64) = nExtra8 in let (va_arg82:Vale.Def.Types_s.nat64) =
va_get_reg64 rR9 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 451 column 28 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_bytes_and_mod va_arg82 va_arg83) (va_qAssertSquash
va_range1
"***** EXPRESSION PRECONDITIONS NOT MET WITHIN line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Prims.pow2 (8 `op_Multiply` nExtra8) >= 0 /\ Prims.pow2 (8 `op_Multiply` nExtra8) <=
18446744073709551615) (fun _ -> let (va_arg81:Vale.Def.Types_s.nat64) = Prims.pow2 (8
`op_Multiply` nExtra8) in let (va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg79:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 452 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_mod_hi va_arg79 va_arg80 va_arg81) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 453 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 454 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 455 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRcx)) (fun (va_s:va_state) _ ->
va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 456 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == inpLast
`op_Modulus` padLast) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 459 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 460 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 461 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 463 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 464 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 465 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbp) (va_const_opr64 0)) (va_QEmpty
(()))))))))))))))))))))))))) (fun (va_s:va_state) va_g -> let (h:int) = hBlocks + inpLast
`op_Modulus` padLast + padLast in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 469 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == va_mul_nat (va_get_reg64 rRbp va_s) (va_mul_nat n n) + va_mul_nat (va_get_reg64 rRbx
va_s) n + va_get_reg64 rR14 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 69 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 469 column 93 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 470 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_mul_nat r1 n + va_get_reg64 rR11 va_s) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 470 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 471 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_iteration r1) (fun (va_s:va_state) (hLast:int) -> va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 472 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(hLast == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 87 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 472 column 111 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg71:Prims.int) = r in let (va_arg70:Prims.int) = inpLast `op_Modulus` padLast + padLast
in let (va_arg69:Prims.pos) = p in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 473 column 21 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_demod va_arg69 hBlocks va_arg70 va_arg71)
(va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 474 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 474 column 90 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (()))) (va_QEmpty (()))))))))))
val va_lemma_Poly1305_last_block : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_last_block ()) va_s0 /\ va_get_ok va_s0 /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16))))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = 18446744073709551616 in let
(p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply`
8) in let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in
Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r))) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM va_s0)))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_last_block va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_last_block va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_last_block ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 380 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 402 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 403 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let padLast = Prims.pow2 (va_get_reg64 rR15 va_sM `op_Multiply` 8) in label va_range1
"***** POSTCONDITION NOT MET AT line 404 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let hLast = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64
rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM) in label va_range1
"***** POSTCONDITION NOT MET AT line 405 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp ((Vale.Poly1305.Spec_s.modp
hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply` r)))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_last_block (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
18446744073709551616 in let (p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819)) = va_mul_nat n n `op_Multiply` 4 - 5 in let
(r1:nat64) = va_get_reg64 rRax va_s0 in let (r:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in let (hBlocks:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0)
(va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let (inpLast:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0) (va_get_reg64 rR9 va_s0) in
va_get_reg64 rRbp va_s0 < 5 /\ va_get_reg64 rR11 va_s0 < n `op_Division` 16 /\ r1 < n
`op_Division` 16 /\ r1 `op_Modulus` 4 == 0 /\ va_get_reg64 rR13 va_s0 == r1 + r1 `op_Division`
4 /\ (1 <= va_get_reg64 rR15 va_s0 /\ va_get_reg64 rR15 va_s0 < 16)) /\ (forall
(va_x_rax:nat64) (va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_r8:nat64) (va_x_r9:nat64)
(va_x_r10:nat64) (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t)
. let va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx
(va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64
rR8 va_x_r8 (va_upd_reg64 rRdx va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax
va_s0))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = 18446744073709551616 in let (p:(va_int_range
1361129467683753853853498429727072845819 1361129467683753853853498429727072845819)) =
va_mul_nat n n `op_Multiply` 4 - 5 in let (r1:nat64) = va_get_reg64 rRax va_s0 in let
(r:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s0) r1 in
let (hBlocks:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in let
(inpLast:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s0)
(va_get_reg64 rR9 va_s0) in va_get_reg64 rRbp va_sM < 5 /\ (let padLast = Prims.pow2
(va_get_reg64 rR15 va_sM `op_Multiply` 8) in let hLast = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM) in Vale.Poly1305.Spec_s.modp hLast == Vale.Poly1305.Spec_s.modp
((Vale.Poly1305.Spec_s.modp hBlocks + padLast + inpLast `op_Modulus` padLast) `op_Multiply`
r))) ==> va_k va_sM (())))
val va_wpProof_Poly1305_last_block : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_last_block va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_last_block ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax])
va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_last_block va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_last_block (va_code_Poly1305_last_block ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM
(va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_last_block () : (va_quickCode unit (va_code_Poly1305_last_block ())) =
(va_QProc (va_code_Poly1305_last_block ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRdx;
va_Mod_reg64 rRcx; va_Mod_reg64 rRax]) va_wp_Poly1305_last_block va_wpProof_Poly1305_last_block)
//--
//-- Poly1305_reduce_last
val va_code_Poly1305_reduce_last : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_reduce_last () =
(va_Block (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_CCons
(va_code_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_CCons
(va_code_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_CCons (va_code_Adc64Wrap
(va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (va_CCons (va_code_Shr64
(va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_CCons (va_code_Sub64Wrap
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_And64
(va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Add64
(va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_reduce_last : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_reduce_last () =
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp))
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax))
(va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0))
(va_pbool_and (va_codegen_success_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64
rR10)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rR8)) (va_pbool_and (va_codegen_success_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64
rR9)) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_reduce_last (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_reduce_last ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (h:Prims.int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 490 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 492 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rR14)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 493 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRbx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 494 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR10) (va_op_opr64_reg64 rRbp)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 495 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR8) (va_const_opr64 5)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 496 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR9) (va_const_opr64 0)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 497 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rR10) (va_const_opr64 0)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 499 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h + 5 == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8
va_s) (va_get_reg64 rR9 va_s)) (va_get_reg64 rR10 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 500 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (let
(va_arg32:Vale.Def.Types_s.nat64) = va_get_reg64 rR8 va_s in let
(va_arg31:Vale.Def.Types_s.nat64) = va_get_reg64 rR9 va_s in let
(va_arg30:Vale.Def.Types_s.nat64) = va_get_reg64 rR10 va_s in let (va_arg29:Prims.int) = h + 5
in let (va_arg28:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in let
(va_arg27:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg26:Vale.Def.Types_s.nat64) = va_get_reg64 rRbp va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 501 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_reduce128 h va_arg26 va_arg27 va_arg28 va_arg29
va_arg30 va_arg31 va_arg32) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 503 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Shr64 (va_op_dst_opr64_reg64 rR10) (va_const_shift_amt64 2)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 505 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 506 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_const_opr64 1)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 508 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 509 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 511 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 0)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 512 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64Wrap (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rR10)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 514 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR8) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 515 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR9) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 518 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rR8)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 519 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64 (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rR9)) (va_QEmpty
(())))))))))))))))))))))))
val va_lemma_Poly1305_reduce_last : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_reduce_last ()) va_s0 /\ va_get_ok va_s0 /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in va_get_reg64
rRbp va_s0 < 5)))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0)) (va_get_reg64 rRbp va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) /\ va_state_eq va_sM
(va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0)))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_reduce_last va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_reduce_last va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_reduce_last ()) va_qc va_s0
(fun va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 478 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in label va_range1
"***** POSTCONDITION NOT MET AT line 488 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_ok]) va_sM
va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_reduce_last (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in va_get_reg64 rRbp va_s0 < 5) /\ (forall (va_x_r8:nat64)
(va_x_r9:nat64) (va_x_r10:nat64) (va_x_rax:nat64) (va_x_r14:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_efl:Vale.X64.Flags.t) . let va_sM = va_upd_flags va_x_efl (va_upd_reg64
rRbp va_x_rbp (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rRax
va_x_rax (va_upd_reg64 rR10 va_x_r10 (va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8
va_s0))))))) in va_get_ok va_sM /\ (let (h:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0))
(va_get_reg64 rRbp va_s0) in Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM)
(va_get_reg64 rRbx va_sM) == Vale.Poly1305.Spec_s.mod2_128 (Vale.Poly1305.Spec_s.modp h)) ==>
va_k va_sM (())))
val va_wpProof_Poly1305_reduce_last : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_reduce_last va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_reduce_last ())
([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_reg64 rRax;
va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_reduce_last va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_reduce_last (va_code_Poly1305_reduce_last ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbp va_sM (va_update_reg64
rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rRax va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_ok va_sM va_s0))))))))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rR14;
va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_reduce_last () : (va_quickCode unit (va_code_Poly1305_reduce_last ())) =
(va_QProc (va_code_Poly1305_reduce_last ()) ([va_Mod_flags; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx;
va_Mod_reg64 rR14; va_Mod_reg64 rRax; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8])
va_wp_Poly1305_reduce_last va_wpProof_Poly1305_reduce_last)
//--
//-- Poly1305_add_key_s
val va_code_Poly1305_add_key_s : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_add_key_s () =
(va_Block (va_CCons (va_code_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax))
(va_CCons (va_code_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (va_CNil
()))))
val va_codegen_success_Poly1305_add_key_s : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_add_key_s () =
(va_pbool_and (va_codegen_success_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64
rRax)) (va_pbool_and (va_codegen_success_Adc64Wrap (va_op_dst_opr64_reg64 rRbx)
(va_op_opr64_reg64 rRdx)) (va_ttrue ())))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_add_key_s (va_mods:va_mods_t) : (va_quickCode unit
(va_code_Poly1305_add_key_s ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let
(h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s) (va_get_reg64 rRdx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 536 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Add64Wrap (va_op_dst_opr64_reg64 rR14) (va_op_opr64_reg64 rRax)) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 537 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Adc64Wrap (va_op_dst_opr64_reg64 rRbx) (va_op_opr64_reg64 rRdx)) (fun (va_s:va_state)
_ -> let (va_arg18:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_s in let
(va_arg17:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_s in let (va_arg16:Prims.int) = key_s
in let (va_arg15:Vale.Def.Types_s.nat64) = va_get_reg64 rRdx va_s in let
(va_arg14:Vale.Def.Types_s.nat64) = va_get_reg64 rRax va_s in let (va_arg13:Prims.int) = h_in
in let (va_arg12:Vale.Def.Types_s.nat64) = va_get_reg64 rRbx va_old_s in let
(va_arg11:Vale.Def.Types_s.nat64) = va_get_reg64 rR14 va_old_s in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 539 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_key va_arg11 va_arg12 va_arg13 va_arg14 va_arg15
va_arg16 va_arg17 va_arg18) (va_QEmpty (()))))))
val va_lemma_Poly1305_add_key_s : va_b0:va_code -> va_s0:va_state
-> Ghost (va_state & va_fuel)
(requires (va_require_total va_b0 (va_code_Poly1305_add_key_s ()) va_s0 /\ va_get_ok va_s0))
(ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) /\ va_state_eq va_sM (va_update_flags va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rR14 va_sM (va_update_ok va_sM va_s0))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_add_key_s va_b0 va_s0 =
let (va_mods:va_mods_t) = [va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok] in
let va_qc = va_qcode_Poly1305_add_key_s va_mods in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_add_key_s ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let () = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 523 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 534 column 56 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14; va_Mod_ok]) va_sM va_s0;
(va_sM, va_fM)
[@ va_qattr]
let va_wp_Poly1305_add_key_s (va_s0:va_state) (va_k:(va_state -> unit -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (forall (va_x_r14:nat64) (va_x_rbx:nat64) (va_x_efl:Vale.X64.Flags.t) . let
va_sM = va_upd_flags va_x_efl (va_upd_reg64 rRbx va_x_rbx (va_upd_reg64 rR14 va_x_r14 va_s0))
in va_get_ok va_sM /\ (let (h_in:Vale.Def.Words_s.nat128) = Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_s0) (va_get_reg64 rRbx va_s0) in let (key_s:Vale.Def.Words_s.nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rRax va_s0) (va_get_reg64 rRdx va_s0) in
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM) ==
Vale.Poly1305.Spec_s.mod2_128 (h_in + key_s)) ==> va_k va_sM (())))
val va_wpProof_Poly1305_add_key_s : va_s0:va_state -> va_k:(va_state -> unit -> Type0)
-> Ghost (va_state & va_fuel & unit)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_add_key_s va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_add_key_s ()) ([va_Mod_flags;
va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_add_key_s va_s0 va_k =
let (va_sM, va_f0) = va_lemma_Poly1305_add_key_s (va_code_Poly1305_add_key_s ()) va_s0 in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_flags va_sM (va_update_reg64 rRbx va_sM (va_update_reg64
rR14 va_sM (va_update_ok va_sM va_s0)))));
va_lemma_norm_mods ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14]) va_sM va_s0;
let va_g = () in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_add_key_s () : (va_quickCode unit (va_code_Poly1305_add_key_s ())) =
(va_QProc (va_code_Poly1305_add_key_s ()) ([va_Mod_flags; va_Mod_reg64 rRbx; va_Mod_reg64 rR14])
va_wp_Poly1305_add_key_s va_wpProof_Poly1305_add_key_s)
//--
// REVIEW: not clear why Vale.Def.TypesNative_s.reveal_iand doesn't work directly
let reveal_logand128 (x y:nat128) : Lemma
(requires True)
(ensures Vale.Def.Types_s.iand x y == FStar.UInt.logand #128 x y)
= Vale.Def.TypesNative_s.reveal_iand 128 x y
//-- reveal_logand128
//--
//-- Poly1305_impl
val va_code_Poly1305_impl : va_dummy:unit -> Tot va_code
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305_impl () =
(va_Block (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64
rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12) (va_op_reg_opr64_reg64 rRdi) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413247)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1152921487695413244)) (va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64
rRcx)) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR12) 32
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx))
(va_CCons (va_code_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_CCons
(va_code_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_CCons
(va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (va_CCons
(va_code_Poly1305_blocks ()) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 184 Public) (va_CCons (va_IfElse
(va_cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (va_Block (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15) (va_op_reg_opr64_reg64 rRdi) 56
Public) (va_CCons (va_IfElse (va_cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (va_Block
(va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_CCons (va_code_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64
rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public) (va_CCons (va_code_Poly1305_last_block ()) (va_CNil
())))))) (va_Block (va_CNil ()))) (va_CCons (va_code_Poly1305_reduce_last ()) (va_CCons
(va_code_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public) (va_CCons (va_code_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48
Public) (va_CCons (va_code_Poly1305_add_key_s ()) (va_CNil ())))))))) (va_Block (va_CNil ())))
(va_CNil ())))))))))))))))))))
val va_codegen_success_Poly1305_impl : va_dummy:unit -> Tot va_pbool
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305_impl () =
(va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rR11) (va_op_reg_opr64_reg64 rRdi) 24 Public) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_pbool_and
(va_codegen_success_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244))
(va_pbool_and (va_codegen_success_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx))
(va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR11) 24 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_pbool_and (va_codegen_success_And64
(va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_pbool_and (va_codegen_success_Sub64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRdx) 64
Public) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64
1)) (va_pbool_and (va_codegen_success_Poly1305_blocks ()) (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public) (va_pbool_and (va_pbool_and
(va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8) (va_op_reg_opr64_reg64 rRsi) 0
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 0)
(va_op_dst_opr64_reg64 rR9) (va_op_reg_opr64_reg64 rRsi) 8 Public)
(va_codegen_success_Poly1305_last_block ())))) (va_pbool_and
(va_codegen_success_Poly1305_reduce_last ()) (va_pbool_and (va_codegen_success_Load64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax) (va_op_reg_opr64_reg64 rRdi) 40
Public) (va_pbool_and (va_codegen_success_Load64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_dst_opr64_reg64 rRdx) (va_op_reg_opr64_reg64 rRdi) 48 Public)
(va_codegen_success_Poly1305_add_key_s ())))))) (va_ttrue ()))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_qcode_Poly1305_impl (va_mods:va_mods_t) (key_r:nat128) (key_s:nat128) (ctx_b:buffer64)
(inp_b:buffer64) (finish:nat64) : (va_quickCode (int) (va_code_Poly1305_impl ())) =
(qblock va_mods (fun (va_s:va_state) -> let (va_old_s:va_state) = va_s in let (n:(va_int_range
18446744073709551616 18446744073709551616)) = pow2_64 in let (inp_in:nat64) = va_get_reg64 rRsi
va_s in let (len_in:nat64) = va_get_reg64 rRdx va_s in let (h0_in:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s) in let
(h1_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1
va_s) in let (h2_in:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 2
(va_get_mem_heaplet 1 va_s) in let (h_in:Prims.int) = Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let (key_r0:Vale.Def.Types_s.nat64) =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s) in let
(key_r1:Vale.Def.Types_s.nat64) = Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1
va_s) in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 607 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_poly_bits64 ()) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 609 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR11)
(va_op_reg_opr64_reg64 rRdi) 24 Public ctx_b 3) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 610 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR12)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 611 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413247)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 612 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 613 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1152921487695413244)) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 614 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rR12) (va_op_opr64_reg64 rRcx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 615 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR11) 24 Public ctx_b 3) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 616 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rR12) 32 Public ctx_b 4) (fun (va_s:va_state) _ -> let (r:nat128) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR11 va_s) (va_get_reg64 rR12 va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 619 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == va_get_reg64 rR11 va_s + va_mul_nat n (va_get_reg64 rR12 va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 619 column 54 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (let
(mask:nat128) = 21267647620597763993911028882763415551 in va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 622 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Arch.Types.iand128 key_r mask) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 624 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (let
(va_arg81:Vale.Def.Types_s.nat64) = va_get_reg64 rR12 va_s in let
(va_arg80:Vale.Def.Types_s.nat64) = va_get_reg64 rR11 va_s in let
(va_arg79:Vale.Def.Words_s.nat128) = r in let (va_arg78:Vale.Def.Words_s.nat128) = mask in let
(va_arg77:Vale.Def.Words_s.nat128) = key_r in va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 625 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_lowerUpper128_and va_arg77 key_r0 key_r1 va_arg78
1152921487695413247 1152921487695413244 va_arg79 va_arg80 va_arg81) (va_QEmpty (())))) (va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 629 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdx)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 630 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_And64 (va_op_dst_opr64_reg64 rRax) (va_const_opr64 15)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 631 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Sub64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rRax)) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 634 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRax) 56 Public ctx_b 7) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 635 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRdx) 64 Public ctx_b 8) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 637 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_const_opr64 1)) (fun (va_s:va_state) _ ->
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 638 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h_in == va_mul_nat h2_in (va_mul_nat n n) + va_mul_nat h1_in n + h0_in) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 81 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 638 column 105 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_QEmpty (())))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 639 column 7 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_blocks r h_in ctx_b inp_b) (fun (va_s:va_state) (h:int) -> va_qAssertBy
va_range1
"***** PRECONDITION NOT MET AT line 640 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14
va_s) (va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s)) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 34 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper192_reveal ()) (va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 641 column 58 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (())))) (let
(va_arg76:Prims.int) = va_get_reg64 rRdx va_old_s `op_Division` 16 in let
(va_arg75:Vale.X64.Memory.buffer64) = inp_b in let (va_arg74:Vale.X64.Memory.vale_heap) =
va_get_mem_heaplet 0 va_s in let (va_arg73:Prims.int) = r in let (va_arg72:Prims.int) =
va_mul_nat n n in let (va_arg71:Prims.int) = Vale.Poly1305.Spec_s.modp h_in in va_qPURE
va_range1
"***** PRECONDITION NOT MET AT line 642 column 40 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Util.lemma_poly1305_heap_hash_blocks_alt va_arg71 va_arg72
va_arg73 va_arg74 va_arg75 va_arg76) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 644 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 184 Public ctx_b 23) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 645 column 8 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_eq (va_op_cmp_reg64 rRax) (va_const_cmp 1)) (qblock va_mods (fun
(va_s:va_state) -> va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 647 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> reveal_logand128 key_r mask) (va_qAssert va_range1
"***** PRECONDITION NOT MET AT line 648 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(r == Vale.Poly1305.Math.bare_r key_r) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 650 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rR15)
(va_op_reg_opr64_reg64 rRdi) 56 Public ctx_b 7) (fun (va_s:va_state) _ -> va_QBind va_range1
"***** PRECONDITION NOT MET AT line 652 column 12 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qIf va_mods (Cmp_ne (va_op_cmp_reg64 rR15) (va_const_cmp 0)) (qblock va_mods (fun
(va_s:va_state) -> va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 654 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 32 Public ctx_b 4) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 655 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR8)
(va_op_reg_opr64_reg64 rRsi) 0 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 656 column 26 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 0) (va_op_dst_opr64_reg64 rR9)
(va_op_reg_opr64_reg64 rRsi) 8 Public inp_b (len_in `op_Division` 16 `op_Multiply` 2 + 1)) (fun
(va_s:va_state) _ -> let (a:Vale.X64.Machine_s.nat128) = Vale.Poly1305.Util.seqTo128_app
(Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s) inp_b) (len_in `op_Division` 16) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 658 column 13 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR8 va_s) (va_get_reg64 rR9 va_s) == a)
(va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 659 column 42 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lowerUpper128_reveal ()) (va_QEmpty (()))) (va_QBind
va_range1
"***** PRECONDITION NOT MET AT line 660 column 32 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_last_block ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s)
(va_get_reg64 rRbx va_s)) (va_get_reg64 rRbp va_s) in va_QEmpty ((h))))))))) (qblock va_mods
(fun (va_s:va_state) -> va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in
let (va_arg70:Prims.int) = key_s in let (va_arg69:Prims.int) = Vale.Poly1305.Spec_s.modp h in
va_qPURE va_range1
"***** PRECONDITION NOT MET AT line 664 column 25 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(fun (_:unit) -> Vale.Poly1305.Math.lemma_add_mod128 va_arg69 va_arg70) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 665 column 29 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_reduce_last ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 668 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRax)
(va_op_reg_opr64_reg64 rRdi) 40 Public ctx_b 5) (va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 669 column 22 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Load64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_dst_opr64_reg64 rRdx)
(va_op_reg_opr64_reg64 rRdi) 48 Public ctx_b 6) (va_QBind va_range1
"***** PRECONDITION NOT MET AT line 670 column 27 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_add_key_s ()) (fun (va_s:va_state) _ -> let (h:int) =
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_s) (va_get_reg64 rRbx va_s) in
va_qAssertBy va_range1
"***** PRECONDITION NOT MET AT line 673 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in) key_r key_s
(Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0 va_s)
inp_b)) len_in) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 18 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%mod2_128) mod2_128 mod2_128) (fun _ -> va_reveal_opaque
(`%mod2_128) mod2_128) (va_QLemma va_range1
"***** PRECONDITION NOT MET AT line 674 column 35 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
true (fun _ -> va_reveal_eq (`%modp) modp modp) (fun _ -> va_reveal_opaque (`%modp) modp)
(va_QEmpty (())))) (va_QEmpty ((h)))))))))))))) (qblock va_mods (fun (va_s:va_state) ->
va_QEmpty ((h))))) (fun (va_s:va_state) va_g -> let (h:int) = va_g in va_QEmpty
((h)))))))))))))))))))))))))))
val va_lemma_Poly1305_impl : va_b0:va_code -> va_s0:va_state -> key_r:nat128 -> key_s:nat128 ->
ctx_b:buffer64 -> inp_b:buffer64 -> finish:nat64
-> Ghost (va_state & va_fuel & int)
(requires (va_require_total va_b0 (va_code_Poly1305_impl ()) va_s0 /\ va_get_ok va_s0 /\ (let
(n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b 24
(va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0 va_s0)
(va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx va_s0))
(va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 < pow2_64
/\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let key_r0
= Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2))))
(ensures (fun (va_sM, va_fM, h) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
(let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64 in
Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public /\ Vale.X64.Decls.modifies_buffer_specific ctx_b
(va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet 1 va_sM) 0 8 /\ (let h0_in =
Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in let h1_in =
Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) /\ va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM
(va_update_reg64 rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM
(va_update_reg64 rR12 va_sM (va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM
(va_update_reg64 rR9 va_sM (va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM
(va_update_reg64 rRbx va_sM (va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM
(va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM
(va_update_ok va_sM (va_update_mem va_sM va_s0)))))))))))))))))))))
[@"opaque_to_smt"]
let va_lemma_Poly1305_impl va_b0 va_s0 key_r key_s ctx_b inp_b finish =
let (va_mods:va_mods_t) = [va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64
rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64
rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64
rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem] in
let va_qc = va_qcode_Poly1305_impl va_mods key_r key_s ctx_b inp_b finish in
let (va_sM, va_fM, va_g) = va_wp_sound_code_norm (va_code_Poly1305_impl ()) va_qc va_s0 (fun
va_s0 va_sM va_g -> let h = va_g in label va_range1
"***** POSTCONDITION NOT MET AT line 551 column 1 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_ok va_sM) /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) =
pow2_64 in label va_range1
"***** POSTCONDITION NOT MET AT line 584 column 66 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM) (va_get_reg64 rRdi va_sM) ctx_b 24
(va_get_mem_layout va_sM) Public) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 585 column 65 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 586 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 587 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 588 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in label
va_range1
"***** POSTCONDITION NOT MET AT line 589 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let h_in = Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in)
h2_in in label va_range1
"***** POSTCONDITION NOT MET AT line 590 column 9 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(let inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet
0 va_sM) inp_b) in label va_range1
"***** POSTCONDITION NOT MET AT line 591 column 70 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128
(va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) (va_get_reg64 rRbp va_sM)) /\ label
va_range1
"***** POSTCONDITION NOT MET AT line 593 column 102 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> Vale.Poly1305.Spec_s.modp h == Vale.Poly1305.Spec_s.poly1305_hash_blocks
(Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n) (Vale.Poly1305.Spec_s.make_r key_r) inp_mem
(va_get_reg64 rRdx va_s0 `op_Division` 16)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 594 column 31 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 595 column 51 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64
rRbx va_sM)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 596 column 92 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ label va_range1
"***** POSTCONDITION NOT MET AT line 597 column 24 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_get_reg64 rRdi va_sM == va_get_reg64 rRdi va_s0)))))))) in
assert_norm (va_qc.mods == va_mods);
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_ok; va_Mod_mem]) va_sM va_s0;
let h = va_g in
(va_sM, va_fM, h)
[@ va_qattr]
let va_wp_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) (va_s0:va_state) (va_k:(va_state -> int -> Type0)) : Type0 =
(va_get_ok va_s0 /\ (let (n:(va_int_range 18446744073709551616 18446744073709551616)) = pow2_64
in Vale.X64.Decls.validDstAddrs64 (va_get_mem_heaplet 1 va_s0) (va_get_reg64 rRdi va_s0) ctx_b
24 (va_get_mem_layout va_s0) Public /\ Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 0
va_s0) (va_get_reg64 rRsi va_s0) inp_b (Vale.Poly1305.Util.readable_words (va_get_reg64 rRdx
va_s0)) (va_get_mem_layout va_s0) Public /\ va_get_reg64 rRsi va_s0 + va_get_reg64 rRdx va_s0 <
pow2_64 /\ (let h2_in = Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in
let key_r0 = Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s0) in let key_r1 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s0) in let key_s0 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s0) in let key_s1 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s0) in finish ==
Vale.X64.Decls.buffer64_read ctx_b 23 (va_get_mem_heaplet 1 va_s0) /\ key_r ==
Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 /\ key_s == Vale.Poly1305.Math.lowerUpper128
key_s0 key_s1 /\ h2_in < 5 /\ finish < 2)) /\ (forall (va_x_mem:vale_heap) (va_x_rax:nat64)
(va_x_rcx:nat64) (va_x_rdx:nat64) (va_x_rdi:nat64) (va_x_rsi:nat64) (va_x_rbx:nat64)
(va_x_rbp:nat64) (va_x_r8:nat64) (va_x_r9:nat64) (va_x_r10:nat64) (va_x_r11:nat64)
(va_x_r12:nat64) (va_x_r13:nat64) (va_x_r14:nat64) (va_x_r15:nat64) (va_x_efl:Vale.X64.Flags.t)
(va_x_heap1:vale_heap) (h:int) . let va_sM = va_upd_mem_heaplet 1 va_x_heap1 (va_upd_flags
va_x_efl (va_upd_reg64 rR15 va_x_r15 (va_upd_reg64 rR14 va_x_r14 (va_upd_reg64 rR13 va_x_r13
(va_upd_reg64 rR12 va_x_r12 (va_upd_reg64 rR11 va_x_r11 (va_upd_reg64 rR10 va_x_r10
(va_upd_reg64 rR9 va_x_r9 (va_upd_reg64 rR8 va_x_r8 (va_upd_reg64 rRbp va_x_rbp (va_upd_reg64
rRbx va_x_rbx (va_upd_reg64 rRsi va_x_rsi (va_upd_reg64 rRdi va_x_rdi (va_upd_reg64 rRdx
va_x_rdx (va_upd_reg64 rRcx va_x_rcx (va_upd_reg64 rRax va_x_rax (va_upd_mem va_x_mem
va_s0))))))))))))))))) in va_get_ok va_sM /\ (let (n:(va_int_range 18446744073709551616
18446744073709551616)) = pow2_64 in Vale.X64.Decls.validSrcAddrs64 (va_get_mem_heaplet 1 va_sM)
(va_get_reg64 rRdi va_sM) ctx_b 24 (va_get_mem_layout va_sM) Public /\
Vale.X64.Decls.modifies_buffer_specific ctx_b (va_get_mem_heaplet 1 va_s0) (va_get_mem_heaplet
1 va_sM) 0 8 /\ (let h0_in = Vale.X64.Decls.buffer64_read ctx_b 0 (va_get_mem_heaplet 1 va_s0)
in let h1_in = Vale.X64.Decls.buffer64_read ctx_b 1 (va_get_mem_heaplet 1 va_s0) in let h2_in =
Vale.X64.Decls.buffer64_read ctx_b 2 (va_get_mem_heaplet 1 va_s0) in let h_in =
Vale.Poly1305.Math.lowerUpper192 (Vale.Poly1305.Math.lowerUpper128 h0_in h1_in) h2_in in let
inp_mem = Vale.Poly1305.Util.seqTo128 (Vale.X64.Decls.buffer64_as_seq (va_get_mem_heaplet 0
va_sM) inp_b) in (finish == 0 ==> h == Vale.Poly1305.Math.lowerUpper192
(Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM))
(va_get_reg64 rRbp va_sM)) /\ (finish == 0 ==> Vale.Poly1305.Spec_s.modp h ==
Vale.Poly1305.Spec_s.poly1305_hash_blocks (Vale.Poly1305.Spec_s.modp h_in) (va_mul_nat n n)
(Vale.Poly1305.Spec_s.make_r key_r) inp_mem (va_get_reg64 rRdx va_s0 `op_Division` 16)) /\
(finish == 0 ==> va_get_reg64 rRbp va_sM < 5) /\ (finish == 1 ==> h ==
Vale.Poly1305.Math.lowerUpper128 (va_get_reg64 rR14 va_sM) (va_get_reg64 rRbx va_sM)) /\
(finish == 1 ==> h == Vale.Poly1305.Spec_s.poly1305_hash_all (Vale.Poly1305.Spec_s.modp h_in)
key_r key_s inp_mem (va_get_reg64 rRdx va_s0)) /\ va_get_reg64 rRdi va_sM == va_get_reg64 rRdi
va_s0)) ==> va_k va_sM ((h))))
val va_wpProof_Poly1305_impl : key_r:nat128 -> key_s:nat128 -> ctx_b:buffer64 -> inp_b:buffer64 ->
finish:nat64 -> va_s0:va_state -> va_k:(va_state -> int -> Type0)
-> Ghost (va_state & va_fuel & int)
(requires (va_t_require va_s0 /\ va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k))
(ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet
1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12;
va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp;
va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx;
va_Mod_reg64 rRax; va_Mod_mem]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@"opaque_to_smt"]
let va_wpProof_Poly1305_impl key_r key_s ctx_b inp_b finish va_s0 va_k =
let (va_sM, va_f0, h) = va_lemma_Poly1305_impl (va_code_Poly1305_impl ()) va_s0 key_r key_s ctx_b
inp_b finish in
va_lemma_upd_update va_sM;
assert (va_state_eq va_sM (va_update_mem_heaplet 1 va_sM (va_update_flags va_sM (va_update_reg64
rR15 va_sM (va_update_reg64 rR14 va_sM (va_update_reg64 rR13 va_sM (va_update_reg64 rR12 va_sM
(va_update_reg64 rR11 va_sM (va_update_reg64 rR10 va_sM (va_update_reg64 rR9 va_sM
(va_update_reg64 rR8 va_sM (va_update_reg64 rRbp va_sM (va_update_reg64 rRbx va_sM
(va_update_reg64 rRsi va_sM (va_update_reg64 rRdi va_sM (va_update_reg64 rRdx va_sM
(va_update_reg64 rRcx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM (va_update_mem
va_sM va_s0))))))))))))))))))));
va_lemma_norm_mods ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15; va_Mod_reg64 rR14;
va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10; va_Mod_reg64 rR9;
va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi; va_Mod_reg64 rRdi;
va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem]) va_sM va_s0;
let va_g = (h) in
(va_sM, va_f0, va_g)
[@ "opaque_to_smt" va_qattr]
let va_quick_Poly1305_impl (key_r:nat128) (key_s:nat128) (ctx_b:buffer64) (inp_b:buffer64)
(finish:nat64) : (va_quickCode int (va_code_Poly1305_impl ())) =
(va_QProc (va_code_Poly1305_impl ()) ([va_Mod_mem_heaplet 1; va_Mod_flags; va_Mod_reg64 rR15;
va_Mod_reg64 rR14; va_Mod_reg64 rR13; va_Mod_reg64 rR12; va_Mod_reg64 rR11; va_Mod_reg64 rR10;
va_Mod_reg64 rR9; va_Mod_reg64 rR8; va_Mod_reg64 rRbp; va_Mod_reg64 rRbx; va_Mod_reg64 rRsi;
va_Mod_reg64 rRdi; va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRax; va_Mod_mem])
(va_wp_Poly1305_impl key_r key_s ctx_b inp_b finish) (va_wpProof_Poly1305_impl key_r key_s
ctx_b inp_b finish))
//--
//-- Poly1305
[@ "opaque_to_smt" va_qattr]
let va_code_Poly1305 win =
(va_Block (va_CCons (va_code_CreateHeaplets ()) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64
rRax) (va_op_opr64_reg64 rRdi)) (va_CCons (va_code_Mov64 (va_op_dst_opr64_reg64 rR11)
(va_op_opr64_reg64 rRsi)) (va_CCons (if win then va_Block (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_CNil ()))))) else va_Block (va_CNil
())) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRcx) 184 Public) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rRbx)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRbp))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR11)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR12))
(va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_CCons (va_code_Push_Secret
(va_op_reg_opr64_reg64 rR14)) (va_CCons (va_code_Push_Secret (va_op_reg_opr64_reg64 rR15))
(va_CCons (va_code_Poly1305_impl ()) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_CCons (va_code_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64
rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_CCons (va_code_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbp) 16
Public) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR15)) (va_CCons
(va_code_Pop_Secret (va_op_dst_opr64_reg64 rR14)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rR12))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRsi)) (va_CCons (va_code_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbp))
(va_CCons (va_code_Pop_Secret (va_op_dst_opr64_reg64 rRbx)) (va_CCons (va_code_Mov64
(va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRax)) (va_CCons (va_code_DestroyHeaplets ())
(va_CNil ())))))))))))))))))))))))))))))
[@ "opaque_to_smt" va_qattr]
let va_codegen_success_Poly1305 win =
(va_pbool_and (va_codegen_success_CreateHeaplets ()) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi)) (va_pbool_and (va_codegen_success_Mov64
(va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi)) (va_pbool_and (if win then va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdi) (va_op_opr64_reg64 rRcx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRsi) (va_op_opr64_reg64 rRdx)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRdx) (va_op_opr64_reg64 rR8)) (va_pbool_and
(va_codegen_success_Mov64 (va_op_dst_opr64_reg64 rRcx) (va_op_opr64_reg64 rR9)) (va_ttrue
())))) else va_ttrue ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRcx) 184
Public) (va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbx))
(va_pbool_and (va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRbp)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rRax)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR11)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR12)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR13)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR14)) (va_pbool_and
(va_codegen_success_Push_Secret (va_op_reg_opr64_reg64 rR15)) (va_pbool_and
(va_codegen_success_Poly1305_impl ()) (va_pbool_and (va_codegen_success_Store64_buffer
(va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rR14) 0
Public) (va_pbool_and (va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi) (va_op_reg_opr64_reg64 rRbx) 8 Public) (va_pbool_and
(va_codegen_success_Store64_buffer (va_op_heaplet_mem_heaplet 1) (va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRbp) 16 Public) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR15)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR14)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR13)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rR12)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRsi)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbp)) (va_pbool_and (va_codegen_success_Pop_Secret
(va_op_dst_opr64_reg64 rRbx)) (va_pbool_and (va_codegen_success_Mov64 (va_op_dst_opr64_reg64
rRdi) (va_op_opr64_reg64 rRax)) (va_pbool_and (va_codegen_success_DestroyHeaplets ()) (va_ttrue
())))))))))))))))))))))))))))) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.QuickCodes.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.InsStack.fsti.checked",
"Vale.X64.InsMem.fsti.checked",
"Vale.X64.InsBasic.fsti.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Poly1305.Util.fsti.checked",
"Vale.Poly1305.Spec_s.fst.checked",
"Vale.Poly1305.Math.fsti.checked",
"Vale.Def.Words_s.fsti.checked",
"Vale.Def.TypesNative_s.fst.checked",
"Vale.Def.Types_s.fst.checked",
"Vale.Def.Opaque_s.fsti.checked",
"Vale.Arch.Types.fsti.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.UInt.fsti.checked",
"FStar.Seq.Base.fsti.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": true,
"source_file": "Vale.Poly1305.X64.fst"
} | [
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Util",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Math",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305.Spec_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCodes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsStack",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsMem",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.InsBasic",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.Types",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Types_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Opaque_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Poly1305",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 40,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
va_mods: Vale.X64.QuickCode.va_mods_t ->
win: Prims.bool ->
ctx_b: Vale.X64.Memory.buffer64 ->
inp_b: Vale.X64.Memory.buffer64 ->
len_in: Vale.X64.Memory.nat64 ->
finish_in: Vale.X64.Memory.nat64
-> Vale.X64.QuickCode.va_quickCode Prims.unit (Vale.Poly1305.X64.va_code_Poly1305 win) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCode.va_mods_t",
"Prims.bool",
"Vale.X64.Memory.buffer64",
"Vale.X64.Memory.nat64",
"Vale.X64.QuickCodes.qblock",
"Prims.unit",
"Prims.Cons",
"Vale.X64.Decls.va_code",
"Vale.X64.InsMem.va_code_CreateHeaplets",
"Vale.X64.InsBasic.va_code_Mov64",
"Vale.X64.Decls.va_op_dst_opr64_reg64",
"Vale.X64.Machine_s.rRax",
"Vale.X64.Decls.va_op_opr64_reg64",
"Vale.X64.Machine_s.rRdi",
"Vale.X64.Machine_s.rR11",
"Vale.X64.Machine_s.rRsi",
"Vale.X64.QuickCodes.if_code",
"Vale.X64.QuickCodes.block",
"Vale.X64.Machine_s.rRcx",
"Vale.X64.Machine_s.rRdx",
"Vale.X64.Machine_s.rR8",
"Vale.X64.Machine_s.rR9",
"Prims.Nil",
"Vale.X64.Machine_s.precode",
"Vale.X64.Decls.ins",
"Vale.X64.Decls.ocmp",
"Vale.X64.InsMem.va_code_Store64_buffer",
"Vale.X64.Decls.va_op_heaplet_mem_heaplet",
"Vale.X64.Decls.va_op_reg_opr64_reg64",
"Vale.Arch.HeapTypes_s.Public",
"Vale.X64.InsStack.va_code_Push_Secret",
"Vale.X64.Machine_s.rRbx",
"Vale.X64.Machine_s.rRbp",
"Vale.X64.Machine_s.rR12",
"Vale.X64.Machine_s.rR13",
"Vale.X64.Machine_s.rR14",
"Vale.X64.Machine_s.rR15",
"Vale.Poly1305.X64.va_code_Poly1305_impl",
"Vale.X64.InsStack.va_code_Pop_Secret",
"Vale.X64.InsMem.va_code_DestroyHeaplets",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.va_QBind",
"Vale.X64.QuickCodes.va_range1",
"Vale.X64.InsMem.va_quick_CreateHeaplets",
"Vale.Arch.HeapImpl.buffer_info",
"Vale.X64.InsMem.declare_buffer64",
"Vale.Arch.HeapImpl.Immutable",
"Vale.Arch.HeapImpl.Mutable",
"Vale.X64.QuickCodes.va_QSeq",
"Vale.X64.InsBasic.va_quick_Mov64",
"Vale.X64.QuickCodes.va_qInlineIf",
"Vale.X64.QuickCodes.va_QEmpty",
"Vale.X64.QuickCodes.quickCodes",
"Vale.X64.InsMem.va_quick_Store64_buffer",
"Vale.X64.InsStack.va_quick_Push_Secret",
"Prims.int",
"Vale.Poly1305.X64.va_quick_Poly1305_impl",
"Vale.X64.InsStack.va_quick_Pop_Secret",
"Vale.X64.InsMem.va_quick_DestroyHeaplets",
"Vale.Def.Words_s.nat128",
"Vale.Poly1305.Math.lowerUpper128",
"Vale.Def.Words_s.nat64",
"Vale.X64.Decls.buffer64_read",
"Vale.X64.Decls.va_get_mem_heaplet",
"Vale.X64.Decls.va_int_range",
"Prims.op_Subtraction",
"Prims.op_Multiply",
"Vale.X64.Decls.va_mul_nat",
"Vale.X64.Decls.va_if",
"Vale.Def.Types_s.nat64",
"Prims.b2t",
"Vale.X64.Decls.va_get_reg64",
"Prims.l_not",
"Vale.X64.State.vale_state",
"Vale.X64.QuickCode.va_quickCode",
"Vale.Poly1305.X64.va_code_Poly1305"
] | [] | false | false | false | false | false | let va_qcode_Poly1305
(va_mods: va_mods_t)
(win: bool)
(ctx_b inp_b: buffer64)
(len_in finish_in: nat64)
: (va_quickCode unit (va_code_Poly1305 win)) =
| (qblock va_mods
(fun (va_s: va_state) ->
let va_old_s:va_state = va_s in
let ctx_in:(va_int_range 0 18446744073709551615) =
va_if win (fun _ -> va_get_reg64 rRcx va_s) (fun _ -> va_get_reg64 rRdi va_s)
in
let inp_in:(va_int_range 0 18446744073709551615) =
va_if win (fun _ -> va_get_reg64 rRdx va_s) (fun _ -> va_get_reg64 rRsi va_s)
in
let n:(va_int_range 18446744073709551616 18446744073709551616) = 18446744073709551616 in
let p:(va_int_range 1361129467683753853853498429727072845819
1361129467683753853853498429727072845819) =
(va_mul_nat n n) `op_Multiply` 4 - 5
in
va_QBind va_range1
"***** PRECONDITION NOT MET AT line 754 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_CreateHeaplets ([
declare_buffer64 inp_b 0 Public Immutable;
declare_buffer64 ctx_b 1 Public Mutable
]))
(fun (va_s: va_state) _ ->
let key_r0:Vale.Def.Types_s.nat64 =
Vale.X64.Decls.buffer64_read ctx_b 3 (va_get_mem_heaplet 1 va_s)
in
let key_r1:Vale.Def.Types_s.nat64 =
Vale.X64.Decls.buffer64_read ctx_b 4 (va_get_mem_heaplet 1 va_s)
in
let key_s0:Vale.Def.Types_s.nat64 =
Vale.X64.Decls.buffer64_read ctx_b 5 (va_get_mem_heaplet 1 va_s)
in
let key_s1:Vale.Def.Types_s.nat64 =
Vale.X64.Decls.buffer64_read ctx_b 6 (va_get_mem_heaplet 1 va_s)
in
let key_r:Vale.Def.Words_s.nat128 = Vale.Poly1305.Math.lowerUpper128 key_r0 key_r1 in
let key_s:Vale.Def.Words_s.nat128 = Vale.Poly1305.Math.lowerUpper128 key_s0 key_s1 in
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 764 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRax) (va_op_opr64_reg64 rRdi))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 765 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rR11) (va_op_opr64_reg64 rRsi))
(fun (va_s: va_state) _ ->
va_QBind va_range1
"***** PRECONDITION NOT MET AT line 766 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_qInlineIf va_mods
win
(qblock va_mods
(fun (va_s: va_state) ->
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 768 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdi)
(va_op_opr64_reg64 rRcx))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 769 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRsi)
(va_op_opr64_reg64 rRdx))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 770 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRdx)
(va_op_opr64_reg64 rR8))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 771 column 14 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Mov64 (va_op_dst_opr64_reg64 rRcx)
(va_op_opr64_reg64 rR9))
(va_QEmpty (())))))))
(qblock va_mods (fun (va_s: va_state) -> va_QEmpty (()))))
(fun (va_s: va_state) va_g ->
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 785 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet 1)
(va_op_reg_opr64_reg64 rRdi)
(va_op_reg_opr64_reg64 rRcx)
184
Public
ctx_b
23)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 788 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbx))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 789 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRbp))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 790 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rRax))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 791 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR11))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 792 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64 rR12
))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 793 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64
rR13))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 794 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64
rR14))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 795 column 16 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Push_Secret (va_op_reg_opr64_reg64
rR15))
(va_QBind va_range1
"***** PRECONDITION NOT MET AT line 797 column 5 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Poly1305_impl key_r
key_s
ctx_b
inp_b
finish_in)
(fun
(va_s: va_state)
(h': int)
->
va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 799 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer (va_op_heaplet_mem_heaplet
1)
(va_op_reg_opr64_reg64
rRdi)
(va_op_reg_opr64_reg64
rR14)
0
Public
ctx_b
0)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 800 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer
(va_op_heaplet_mem_heaplet
1)
(va_op_reg_opr64_reg64
rRdi)
(va_op_reg_opr64_reg64
rRbx)
8
Public
ctx_b
1)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 801 column 19 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Store64_buffer
(va_op_heaplet_mem_heaplet
1)
(va_op_reg_opr64_reg64
rRdi)
(va_op_reg_opr64_reg64
rRbp)
16
Public
ctx_b
2)
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 804 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret
(va_op_dst_opr64_reg64
rR15))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 805 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret
(va_op_dst_opr64_reg64
rR14
))
(va_QSeq va_range1
"***** PRECONDITION NOT MET AT line 806 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret
(va_op_dst_opr64_reg64
rR13
))
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 807 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(va_quick_Pop_Secret
(
va_op_dst_opr64_reg64
rR12
)
)
(va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 808 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Pop_Secret
(
va_op_dst_opr64_reg64
rRsi
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 809 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Pop_Secret
(
va_op_dst_opr64_reg64
rRax
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 810 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Pop_Secret
(
va_op_dst_opr64_reg64
rRbp
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 811 column 15 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Pop_Secret
(
va_op_dst_opr64_reg64
rRbx
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 813 column 10 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_Mov64
(
va_op_dst_opr64_reg64
rRdi
)
(
va_op_opr64_reg64
rRax
)
)
(
va_QSeq
va_range1
"***** PRECONDITION NOT MET AT line 815 column 20 of file /home/gebner/fstar_dataset/projects/hacl-star/vale/code/thirdPartyPorts/OpenSSL/poly1305/x64/Vale.Poly1305.X64.vaf *****"
(
va_quick_DestroyHeaplets
()
)
(
va_QEmpty
(
()
)
)
)
)
)
)
)
))
))))))))))
))))))))))) | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.va_QBind | val va_QBind
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: (va_state -> b -> GTot (quickCodes a cs)))
: quickCodes a (c :: cs) | val va_QBind
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: (va_state -> b -> GTot (quickCodes a cs)))
: quickCodes a (c :: cs) | let va_QBind (#a:Type0) (#b:Type) (#c:code) (#cs:codes) (r:range) (msg:string) (qc:quickCode b c) (qcs:va_state -> b -> GTot (quickCodes a cs)) : quickCodes a (c::cs) = QBind r msg qc qcs | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 206,
"end_line": 72,
"start_col": 19,
"start_line": 72
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)]
// wrap "precedes" and LexCons to avoid issues with label (precedes ...)
let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y
[@va_qattr]
let rec mods_contains1 (allowed:mods_t) (found:mod_t) : bool =
match allowed with
| [] -> mod_eq Mod_None found
| h::t -> mod_eq h found || mods_contains1 t found
[@va_qattr]
let rec mods_contains (allowed:mods_t) (found:mods_t) : bool =
match found with
| [] -> true
| h::t -> mods_contains1 allowed h && mods_contains allowed t
[@va_qattr]
let if_code (b:bool) (c1:code) (c2:code) : code = if b then c1 else c2
open FStar.Monotonic.Pure
noeq type quickCodes (a:Type0) : codes -> Type =
| QEmpty: a -> quickCodes a []
| QSeq: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> quickCodes a cs -> quickCodes a (c::cs)
| QBind: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a (c::cs)
| QGetState: #cs:codes -> (va_state -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QPURE: #cs:codes -> r:range -> msg:string -> pre:((unit -> GTot Type0) -> GTot Type0){is_monotonic pre} ->
(unit -> PURE unit (as_pure_wp pre)) -> quickCodes a cs -> quickCodes a cs
//| QBindPURE: #cs:codes -> b:Type -> r:range -> msg:string -> pre:((b -> GTot Type0) -> GTot Type0) ->
// (unit -> PURE b pre) -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QLemma: #cs:codes -> r:range -> msg:string -> pre:Type0 -> post:(squash pre -> Type0) ->
(unit -> Lemma (requires pre) (ensures post ())) -> quickCodes a cs -> quickCodes a cs
| QGhost: #cs:codes -> b:Type -> r:range -> msg:string -> pre:Type0 -> post:(b -> Type0) ->
(unit -> Ghost b (requires pre) (ensures post)) -> (b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QAssertBy: #cs:codes -> r:range -> msg:string -> p:Type0 ->
quickCodes unit [] -> quickCodes a cs -> quickCodes a cs | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "FStar.Monotonic.Pure",
"short_module": null
},
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
r: FStar.Range.range ->
msg: Prims.string ->
qc: Vale.X64.QuickCode.quickCode b c ->
qcs: (_: Vale.X64.Decls.va_state -> _: b -> Prims.GTot (Vale.X64.QuickCodes.quickCodes a cs))
-> Vale.X64.QuickCodes.quickCodes a (c :: cs) | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCodes.code",
"Vale.X64.QuickCodes.codes",
"FStar.Range.range",
"Prims.string",
"Vale.X64.QuickCode.quickCode",
"Vale.X64.Decls.va_state",
"Vale.X64.QuickCodes.quickCodes",
"Vale.X64.QuickCodes.QBind",
"Prims.Cons",
"Vale.X64.Decls.va_code"
] | [] | false | false | false | false | false | let va_QBind
(#a: Type0)
(#b: Type)
(#c: code)
(#cs: codes)
(r: range)
(msg: string)
(qc: quickCode b c)
(qcs: (va_state -> b -> GTot (quickCodes a cs)))
: quickCodes a (c :: cs) =
| QBind r msg qc qcs | false |
Vale.X64.QuickCodes.fsti | Vale.X64.QuickCodes.wp_proc | val wp_proc (#a: Type0) (c: code) (qc: quickCode a c) (s0: va_state) (k: (va_state -> a -> Type0))
: Type0 | val wp_proc (#a: Type0) (c: code) (qc: quickCode a c) (s0: va_state) (k: (va_state -> a -> Type0))
: Type0 | let wp_proc (#a:Type0) (c:code) (qc:quickCode a c) (s0:va_state) (k:va_state -> a -> Type0) : Type0 =
match qc with
| QProc _ _ wp _ -> wp s0 k | {
"file_name": "vale/code/arch/x64/Vale.X64.QuickCodes.fsti",
"git_rev": "eb1badfa34c70b0bbe0fe24fe0f49fb1295c7872",
"git_url": "https://github.com/project-everest/hacl-star.git",
"project_name": "hacl-star"
} | {
"end_col": 29,
"end_line": 97,
"start_col": 0,
"start_line": 95
} | module Vale.X64.QuickCodes
// Optimized weakest precondition generation for 'quick' procedures
open FStar.Mul
open FStar.Range
open Vale.Def.Prop_s
open Vale.Arch.HeapImpl
open Vale.X64.Machine_s
open Vale.X64.Memory
open Vale.X64.Stack_i
open Vale.X64.State
open Vale.X64.Decls
open Vale.X64.QuickCode
unfold let code = va_code
unfold let codes = va_codes
unfold let fuel = va_fuel
unfold let eval = eval_code
[@va_qattr "opaque_to_smt"]
let labeled_wrap (r:range) (msg:string) (p:Type0) : GTot Type0 = labeled r msg p
// REVIEW: when used inside a function definition, 'labeled' can show up in an SMT query
// as an uninterpreted function. Make a wrapper around labeled that is interpreted:
[@va_qattr "opaque_to_smt"]
let label (r:range) (msg:string) (p:Type0) : Ghost Type (requires True) (ensures fun q -> q <==> p) =
assert_norm (labeled_wrap r msg p <==> p);
labeled_wrap r msg p
val lemma_label_bool (r:range) (msg:string) (b:bool) : Lemma
(requires label r msg b)
(ensures b)
[SMTPat (label r msg b)]
// wrap "precedes" and LexCons to avoid issues with label (precedes ...)
let precedes_wrap (#a:Type) (x y:a) : GTot Type0 = precedes x y
[@va_qattr]
let rec mods_contains1 (allowed:mods_t) (found:mod_t) : bool =
match allowed with
| [] -> mod_eq Mod_None found
| h::t -> mod_eq h found || mods_contains1 t found
[@va_qattr]
let rec mods_contains (allowed:mods_t) (found:mods_t) : bool =
match found with
| [] -> true
| h::t -> mods_contains1 allowed h && mods_contains allowed t
[@va_qattr]
let if_code (b:bool) (c1:code) (c2:code) : code = if b then c1 else c2
open FStar.Monotonic.Pure
noeq type quickCodes (a:Type0) : codes -> Type =
| QEmpty: a -> quickCodes a []
| QSeq: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> quickCodes a cs -> quickCodes a (c::cs)
| QBind: #b:Type -> #c:code -> #cs:codes -> r:range -> msg:string ->
quickCode b c -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a (c::cs)
| QGetState: #cs:codes -> (va_state -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QPURE: #cs:codes -> r:range -> msg:string -> pre:((unit -> GTot Type0) -> GTot Type0){is_monotonic pre} ->
(unit -> PURE unit (as_pure_wp pre)) -> quickCodes a cs -> quickCodes a cs
//| QBindPURE: #cs:codes -> b:Type -> r:range -> msg:string -> pre:((b -> GTot Type0) -> GTot Type0) ->
// (unit -> PURE b pre) -> (va_state -> b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QLemma: #cs:codes -> r:range -> msg:string -> pre:Type0 -> post:(squash pre -> Type0) ->
(unit -> Lemma (requires pre) (ensures post ())) -> quickCodes a cs -> quickCodes a cs
| QGhost: #cs:codes -> b:Type -> r:range -> msg:string -> pre:Type0 -> post:(b -> Type0) ->
(unit -> Ghost b (requires pre) (ensures post)) -> (b -> GTot (quickCodes a cs)) -> quickCodes a ((Block [])::cs)
| QAssertBy: #cs:codes -> r:range -> msg:string -> p:Type0 ->
quickCodes unit [] -> quickCodes a cs -> quickCodes a cs
[@va_qattr] unfold let va_QBind (#a:Type0) (#b:Type) (#c:code) (#cs:codes) (r:range) (msg:string) (qc:quickCode b c) (qcs:va_state -> b -> GTot (quickCodes a cs)) : quickCodes a (c::cs) = QBind r msg qc qcs
[@va_qattr] unfold let va_QEmpty (#a:Type0) (v:a) : quickCodes a [] = QEmpty v
[@va_qattr] unfold let va_QLemma (#a:Type0) (#cs:codes) (r:range) (msg:string) (pre:Type0) (post:(squash pre -> Type0)) (l:unit -> Lemma (requires pre) (ensures post ())) (qcs:quickCodes a cs) : quickCodes a cs = QLemma r msg pre post l qcs
[@va_qattr] unfold let va_QSeq (#a:Type0) (#b:Type) (#c:code) (#cs:codes) (r:range) (msg:string) (qc:quickCode b c) (qcs:quickCodes a cs) : quickCodes a (c::cs) = QSeq r msg qc qcs
[@va_qattr]
let va_qPURE
(#cs:codes) (#pre:((unit -> GTot Type0) -> GTot Type0){is_monotonic pre}) (#a:Type0) (r:range) (msg:string)
($l:unit -> PURE unit (intro_pure_wp_monotonicity pre; pre)) (qcs:quickCodes a cs)
: quickCodes a cs =
QPURE r msg pre l qcs
(* REVIEW: this might be useful, but inference of pre doesn't work as well as for va_qPURE
(need to provide pre explicitly; as a result, no need to put $ on l)
[@va_qattr]
let va_qBindPURE
(#a #b:Type0) (#cs:codes) (pre:(b -> GTot Type0) -> GTot Type0) (r:range) (msg:string)
(l:unit -> PURE b pre) (qcs:va_state -> b -> GTot (quickCodes a cs))
: quickCodes a ((Block [])::cs) =
QBindPURE b r msg pre l qcs
*) | {
"checked_file": "/",
"dependencies": [
"Vale.X64.State.fsti.checked",
"Vale.X64.Stack_i.fsti.checked",
"Vale.X64.Regs.fsti.checked",
"Vale.X64.QuickCode.fst.checked",
"Vale.X64.Memory.fsti.checked",
"Vale.X64.Machine_s.fst.checked",
"Vale.X64.Flags.fsti.checked",
"Vale.X64.Decls.fsti.checked",
"Vale.Def.Prop_s.fst.checked",
"Vale.Arch.HeapImpl.fsti.checked",
"prims.fst.checked",
"FStar.Range.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Monotonic.Pure.fst.checked",
"FStar.FunctionalExtensionality.fsti.checked",
"FStar.Classical.fsti.checked"
],
"interface_file": false,
"source_file": "Vale.X64.QuickCodes.fsti"
} | [
{
"abbrev": false,
"full_module": "FStar.Monotonic.Pure",
"short_module": null
},
{
"abbrev": true,
"full_module": "Vale.Lib.Map16",
"short_module": "Map16"
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.QuickCode",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Decls",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.State",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Stack_i",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Memory",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64.Machine_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Arch.HeapImpl",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.Def.Prop_s",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Range",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "Vale.X64",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 0,
"max_fuel": 1,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": true,
"smtencoding_l_arith_repr": "native",
"smtencoding_nl_arith_repr": "wrapped",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [
"smt.arith.nl=false",
"smt.QI.EAGER_THRESHOLD=100",
"smt.CASE_SPLIT=3"
],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | false |
c: Vale.X64.QuickCodes.code ->
qc: Vale.X64.QuickCode.quickCode a c ->
s0: Vale.X64.Decls.va_state ->
k: (_: Vale.X64.Decls.va_state -> _: a -> Type0)
-> Type0 | Prims.Tot | [
"total"
] | [] | [
"Vale.X64.QuickCodes.code",
"Vale.X64.QuickCode.quickCode",
"Vale.X64.Decls.va_state",
"Vale.X64.Decls.va_code",
"Vale.X64.QuickCode.mods_t",
"Vale.X64.QuickCode.quickProc_wp",
"Vale.X64.QuickCode.t_proof"
] | [] | false | false | false | false | true | let wp_proc (#a: Type0) (c: code) (qc: quickCode a c) (s0: va_state) (k: (va_state -> a -> Type0))
: Type0 =
| match qc with | QProc _ _ wp _ -> wp s0 k | false |
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